The unit vector in the northeast direction.

Question

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Answer 1

Question

Chapter 1, Problem 60P

(a)

To determine

The unit vector in the northeast direction.

(a)

Expert Solution

Answer to Problem 60P

The unit vector in the northeast direction is $12i^+12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the northeast direction, it will have an angle $45°$ with $+x$ axis.

Calculation:

Substitute $1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=1cos45°i^+1sin45°j^=12i^+12j^$

Conclusion:

Thus, the unit vector in the northeast direction is $12i^+12j^$ .

(b)

To determine

The unit vector in $70°$ clockwise from $−y$ axis.

(b)

Expert Solution

Answer to Problem 60P

The unit vector in $70°$ clockwise from $−y$ axis is $−32i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in $70°$ clockwise from $−y$ axis it will make $30°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $30°$ for $θ$ in equation (1).

$v→=−cos30°i^−1sin30°j^=−32i^−12j^$

Conclusion:

Thus,the unit vector in $70°$ clockwise from $−y$ axis. $−32i^−12j^$ .

To determine

The unit vector in the southwest direction.

Expert Solution

Answer to Problem 60P

The unit vector in the southwest direction is $−12i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

Magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the southwest direction, it will have an angle $45°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=−1cos45°i^−1sin45°j^=−12i^−12j^$

Conclusion:

Thus, the unit vector in the southwest direction is $−12i^−12j^$ .

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Answer 2

Question

Chapter 1, Problem 60P

(a)

To determine

The unit vector in the northeast direction.

(a)

Expert Solution

Answer to Problem 60P

The unit vector in the northeast direction is $12i^+12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the northeast direction, it will have an angle $45°$ with $+x$ axis.

Calculation:

Substitute $1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=1cos45°i^+1sin45°j^=12i^+12j^$

Conclusion:

Thus, the unit vector in the northeast direction is $12i^+12j^$ .

(b)

To determine

The unit vector in $70°$ clockwise from $−y$ axis.

(b)

Expert Solution

Answer to Problem 60P

The unit vector in $70°$ clockwise from $−y$ axis is $−32i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in $70°$ clockwise from $−y$ axis it will make $30°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $30°$ for $θ$ in equation (1).

$v→=−cos30°i^−1sin30°j^=−32i^−12j^$

Conclusion:

Thus,the unit vector in $70°$ clockwise from $−y$ axis. $−32i^−12j^$ .

To determine

The unit vector in the southwest direction.

Expert Solution

Answer to Problem 60P

The unit vector in the southwest direction is $−12i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

Magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the southwest direction, it will have an angle $45°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=−1cos45°i^−1sin45°j^=−12i^−12j^$

Conclusion:

Thus, the unit vector in the southwest direction is $−12i^−12j^$ .

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Answer 3

Question

Chapter 1, Problem 60P

(a)

To determine

The unit vector in the northeast direction.

(a)

Expert Solution

Answer to Problem 60P

The unit vector in the northeast direction is $12i^+12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the northeast direction, it will have an angle $45°$ with $+x$ axis.

Calculation:

Substitute $1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=1cos45°i^+1sin45°j^=12i^+12j^$

Conclusion:

Thus, the unit vector in the northeast direction is $12i^+12j^$ .

(b)

To determine

The unit vector in $70°$ clockwise from $−y$ axis.

(b)

Expert Solution

Answer to Problem 60P

The unit vector in $70°$ clockwise from $−y$ axis is $−32i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in $70°$ clockwise from $−y$ axis it will make $30°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $30°$ for $θ$ in equation (1).

$v→=−cos30°i^−1sin30°j^=−32i^−12j^$

Conclusion:

Thus,the unit vector in $70°$ clockwise from $−y$ axis. $−32i^−12j^$ .

To determine

The unit vector in the southwest direction.

Expert Solution

Answer to Problem 60P

The unit vector in the southwest direction is $−12i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

Magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the southwest direction, it will have an angle $45°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=−1cos45°i^−1sin45°j^=−12i^−12j^$

Conclusion:

Thus, the unit vector in the southwest direction is $−12i^−12j^$ .

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Answer 4

Question

Chapter 1, Problem 60P

(a)

To determine

The unit vector in the northeast direction.

(a)

Expert Solution

Answer to Problem 60P

The unit vector in the northeast direction is $12i^+12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the northeast direction, it will have an angle $45°$ with $+x$ axis.

Calculation:

Substitute $1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=1cos45°i^+1sin45°j^=12i^+12j^$

Conclusion:

Thus, the unit vector in the northeast direction is $12i^+12j^$ .

(b)

To determine

The unit vector in $70°$ clockwise from $−y$ axis.

(b)

Expert Solution

Answer to Problem 60P

The unit vector in $70°$ clockwise from $−y$ axis is $−32i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in $70°$ clockwise from $−y$ axis it will make $30°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $30°$ for $θ$ in equation (1).

$v→=−cos30°i^−1sin30°j^=−32i^−12j^$

Conclusion:

Thus,the unit vector in $70°$ clockwise from $−y$ axis. $−32i^−12j^$ .

To determine

The unit vector in the southwest direction.

Expert Solution

Answer to Problem 60P

The unit vector in the southwest direction is $−12i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

Magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the southwest direction, it will have an angle $45°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=−1cos45°i^−1sin45°j^=−12i^−12j^$

Conclusion:

Thus, the unit vector in the southwest direction is $−12i^−12j^$ .

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Answer 5

Chapter 1, Problem 60P

(a)

To determine

The unit vector in the northeast direction.

(a)

Expert Solution

Answer to Problem 60P

The unit vector in the northeast direction is $12i^+12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the northeast direction, it will have an angle $45°$ with $+x$ axis.

Calculation:

Substitute $1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=1cos45°i^+1sin45°j^=12i^+12j^$

Conclusion:

Thus, the unit vector in the northeast direction is $12i^+12j^$ .

(b)

To determine

The unit vector in $70°$ clockwise from $−y$ axis.

(b)

Expert Solution

Answer to Problem 60P

The unit vector in $70°$ clockwise from $−y$ axis is $−32i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in $70°$ clockwise from $−y$ axis it will make $30°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $30°$ for $θ$ in equation (1).

$v→=−cos30°i^−1sin30°j^=−32i^−12j^$

Conclusion:

Thus,the unit vector in $70°$ clockwise from $−y$ axis. $−32i^−12j^$ .

To determine

The unit vector in the southwest direction.

Expert Solution

Answer to Problem 60P

The unit vector in the southwest direction is $−12i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

Magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the southwest direction, it will have an angle $45°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=−1cos45°i^−1sin45°j^=−12i^−12j^$

Conclusion:

Thus, the unit vector in the southwest direction is $−12i^−12j^$ .

Answer 6

Chapter 1, Problem 60P

(a)

To determine

The unit vector in the northeast direction.

(a)

Expert Solution

Answer to Problem 60P

The unit vector in the northeast direction is $12i^+12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the northeast direction, it will have an angle $45°$ with $+x$ axis.

Calculation:

Substitute $1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=1cos45°i^+1sin45°j^=12i^+12j^$

Conclusion:

Thus, the unit vector in the northeast direction is $12i^+12j^$ .

Answer 7

Chapter 1, Problem 60P

(a)

To determine

The unit vector in the northeast direction.

Answer 8

(a)

Expert Solution

Answer to Problem 60P

The unit vector in the northeast direction is $12i^+12j^$ .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the northeast direction, it will have an angle $45°$ with $+x$ axis.

Calculation:

Substitute $1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=1cos45°i^+1sin45°j^=12i^+12j^$

Conclusion:

Thus, the unit vector in the northeast direction is $12i^+12j^$ .

Answer 13

(b)

To determine

The unit vector in $70°$ clockwise from $−y$ axis.

(b)

Expert Solution

Answer to Problem 60P

The unit vector in $70°$ clockwise from $−y$ axis is $−32i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in $70°$ clockwise from $−y$ axis it will make $30°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $30°$ for $θ$ in equation (1).

$v→=−cos30°i^−1sin30°j^=−32i^−12j^$

Conclusion:

Thus,the unit vector in $70°$ clockwise from $−y$ axis. $−32i^−12j^$ .

Answer 14

(b)

To determine

The unit vector in $70°$ clockwise from $−y$ axis.

Answer 15

(b)

Expert Solution

Answer to Problem 60P

The unit vector in $70°$ clockwise from $−y$ axis is $−32i^−12j^$ .

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

The magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in $70°$ clockwise from $−y$ axis it will make $30°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $30°$ for $θ$ in equation (1).

$v→=−cos30°i^−1sin30°j^=−32i^−12j^$

Conclusion:

Thus,the unit vector in $70°$ clockwise from $−y$ axis. $−32i^−12j^$ .

Answer 20

To determine

The unit vector in the southwest direction.

Expert Solution

Answer to Problem 60P

The unit vector in the southwest direction is $−12i^−12j^$ .

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

Magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the southwest direction, it will have an angle $45°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=−1cos45°i^−1sin45°j^=−12i^−12j^$

Conclusion:

Thus, the unit vector in the southwest direction is $−12i^−12j^$ .

Answer 21

To determine

The unit vector in the southwest direction.

Answer 22

Expert Solution

Answer to Problem 60P

The unit vector in the southwest direction is $−12i^−12j^$ .

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

Unit vectors $i^$ and $j^$ are directed in east and north direction respectively.

Formula used:

Magnitude of unit vector is always equal to one that’s why it is termed as a unit vector.

The general expression for a vector is $v→=vx i^+vyj^$ .

Write the expression for vector in terms of its components.

$v→=vcosθi^+vsinθj^$ ............... (1)

Here, $v→$ is the vector and $v$ is the magnitude of vector.

When the unit vector is in the southwest direction, it will have an angle $45°$ with $−x$ axis.

Calculation:

Substitute $−1$ for $v$ and $45°$ for $θ$ in equation (1).

$v→=−1cos45°i^−1sin45°j^=−12i^−12j^$

Conclusion:

Thus, the unit vector in the southwest direction is $−12i^−12j^$ .

Answer 27

Ch. 1 - Prob. 1P Ch. 1 - Prob. 2P Ch. 1 - Prob. 3P Ch. 1 - Prob. 4P Ch. 1 - Prob. 5P Ch. 1 - Prob. 6P Ch. 1 - Prob. 7P Ch. 1 - Prob. 8P Ch. 1 - Prob. 9P Ch. 1 - Prob. 10P

The unit vector in the northeast direction.

Concept explainers

Videos

The unit vector in the northeast direction.

Answer to Problem 60P

Explanation of Solution

The unit vector in $70°$ clockwise from $−y$ axis.

Answer to Problem 60P

Explanation of Solution

The unit vector in the southwest direction.

Answer to Problem 60P

Explanation of Solution

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Chapter 1 Solutions

The unit vector in the northeast direction.

Concept explainers

Videos

The unit vector in the northeast direction.

Answer to Problem 60P

Explanation of Solution

The unit vector in 70°<m:math><m:mrow><m:mn>70</m:mn><m:mo>°</m:mo></m:mrow></m:math> clockwise from −y<m:math><m:mrow><m:mo>−</m:mo><m:mi>y</m:mi></m:mrow></m:math> axis.

Answer to Problem 60P

Explanation of Solution

The unit vector in the southwest direction.

Answer to Problem 60P

Explanation of Solution

Want to see more full solutions like this?

Chapter 1 Solutions

The unit vector in $70°$ clockwise from $−y$ axis.