The vector A → in component form.

Question

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Answer 1

Question

Chapter 3, Problem 39PQ

(a)

To determine

The vector A→ in component form.

(a)

Expert Solution

Answer to Problem 39PQ

The vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Explanation of Solution

Write the expression to find the component form of any vector.

A→=xi^+yj^+zk^

Here, x is the x component of the vector, y is the y component of the vector and z is the z component of the vector.

Conclusion:

Substitute 15.0 m for x, −6.00 m for y and −3.00 m for z in the above equation.

A→=(15.0 m)i^+(−6.00 m)j^+(−3.00 m)k^=(15.0i^−6.00j^−3.00k^) m

Therefore, the vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

(b)

To determine

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→.

(b)

Expert Solution

Answer to Problem 39PQ

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Explanation of Solution

Write the expression to find the vector B→.

B→=13A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

B→=13((15.0i^−6.00j^−3.00k^) m)=(5.0i^−2.00j^−1.00k^) m

Therefore, the vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

(c)

To determine

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→.

(c)

Expert Solution

Answer to Problem 39PQ

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Explanation of Solution

Write the expression to find the vector C→.

C→=−3A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

C→=−3((15.0i^−6.00j^−3.00k^) m)=(−45.00i^+18.0j^+9.00k^) m

Therefore, the vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

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Answer 2

Question

Chapter 3, Problem 39PQ

(a)

To determine

The vector A→ in component form.

(a)

Expert Solution

Answer to Problem 39PQ

The vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Explanation of Solution

Write the expression to find the component form of any vector.

A→=xi^+yj^+zk^

Here, x is the x component of the vector, y is the y component of the vector and z is the z component of the vector.

Conclusion:

Substitute 15.0 m for x, −6.00 m for y and −3.00 m for z in the above equation.

A→=(15.0 m)i^+(−6.00 m)j^+(−3.00 m)k^=(15.0i^−6.00j^−3.00k^) m

Therefore, the vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

(b)

To determine

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→.

(b)

Expert Solution

Answer to Problem 39PQ

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Explanation of Solution

Write the expression to find the vector B→.

B→=13A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

B→=13((15.0i^−6.00j^−3.00k^) m)=(5.0i^−2.00j^−1.00k^) m

Therefore, the vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

(c)

To determine

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→.

(c)

Expert Solution

Answer to Problem 39PQ

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Explanation of Solution

Write the expression to find the vector C→.

C→=−3A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

C→=−3((15.0i^−6.00j^−3.00k^) m)=(−45.00i^+18.0j^+9.00k^) m

Therefore, the vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

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Answer 3

Question

Chapter 3, Problem 39PQ

(a)

To determine

The vector A→ in component form.

(a)

Expert Solution

Answer to Problem 39PQ

The vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Explanation of Solution

Write the expression to find the component form of any vector.

A→=xi^+yj^+zk^

Here, x is the x component of the vector, y is the y component of the vector and z is the z component of the vector.

Conclusion:

Substitute 15.0 m for x, −6.00 m for y and −3.00 m for z in the above equation.

A→=(15.0 m)i^+(−6.00 m)j^+(−3.00 m)k^=(15.0i^−6.00j^−3.00k^) m

Therefore, the vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

(b)

To determine

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→.

(b)

Expert Solution

Answer to Problem 39PQ

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Explanation of Solution

Write the expression to find the vector B→.

B→=13A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

B→=13((15.0i^−6.00j^−3.00k^) m)=(5.0i^−2.00j^−1.00k^) m

Therefore, the vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

(c)

To determine

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→.

(c)

Expert Solution

Answer to Problem 39PQ

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Explanation of Solution

Write the expression to find the vector C→.

C→=−3A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

C→=−3((15.0i^−6.00j^−3.00k^) m)=(−45.00i^+18.0j^+9.00k^) m

Therefore, the vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

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Answer 4

Question

Chapter 3, Problem 39PQ

(a)

To determine

The vector A→ in component form.

(a)

Expert Solution

Answer to Problem 39PQ

The vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Explanation of Solution

Write the expression to find the component form of any vector.

A→=xi^+yj^+zk^

Here, x is the x component of the vector, y is the y component of the vector and z is the z component of the vector.

Conclusion:

Substitute 15.0 m for x, −6.00 m for y and −3.00 m for z in the above equation.

A→=(15.0 m)i^+(−6.00 m)j^+(−3.00 m)k^=(15.0i^−6.00j^−3.00k^) m

Therefore, the vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

(b)

To determine

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→.

(b)

Expert Solution

Answer to Problem 39PQ

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Explanation of Solution

Write the expression to find the vector B→.

B→=13A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

B→=13((15.0i^−6.00j^−3.00k^) m)=(5.0i^−2.00j^−1.00k^) m

Therefore, the vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

(c)

To determine

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→.

(c)

Expert Solution

Answer to Problem 39PQ

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Explanation of Solution

Write the expression to find the vector C→.

C→=−3A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

C→=−3((15.0i^−6.00j^−3.00k^) m)=(−45.00i^+18.0j^+9.00k^) m

Therefore, the vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

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Answer 5

Chapter 3, Problem 39PQ

(a)

To determine

The vector A→ in component form.

(a)

Expert Solution

Answer to Problem 39PQ

The vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Explanation of Solution

Write the expression to find the component form of any vector.

A→=xi^+yj^+zk^

Here, x is the x component of the vector, y is the y component of the vector and z is the z component of the vector.

Conclusion:

Substitute 15.0 m for x, −6.00 m for y and −3.00 m for z in the above equation.

A→=(15.0 m)i^+(−6.00 m)j^+(−3.00 m)k^=(15.0i^−6.00j^−3.00k^) m

Therefore, the vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

(b)

To determine

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→.

(b)

Expert Solution

Answer to Problem 39PQ

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Explanation of Solution

Write the expression to find the vector B→.

B→=13A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

B→=13((15.0i^−6.00j^−3.00k^) m)=(5.0i^−2.00j^−1.00k^) m

Therefore, the vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

(c)

To determine

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→.

(c)

Expert Solution

Answer to Problem 39PQ

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Explanation of Solution

Write the expression to find the vector C→.

C→=−3A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

C→=−3((15.0i^−6.00j^−3.00k^) m)=(−45.00i^+18.0j^+9.00k^) m

Therefore, the vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Answer 6

Chapter 3, Problem 39PQ

(a)

To determine

The vector A→ in component form.

(a)

Expert Solution

Answer to Problem 39PQ

The vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Explanation of Solution

Write the expression to find the component form of any vector.

A→=xi^+yj^+zk^

Here, x is the x component of the vector, y is the y component of the vector and z is the z component of the vector.

Conclusion:

Substitute 15.0 m for x, −6.00 m for y and −3.00 m for z in the above equation.

A→=(15.0 m)i^+(−6.00 m)j^+(−3.00 m)k^=(15.0i^−6.00j^−3.00k^) m

Therefore, the vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Answer 7

Chapter 3, Problem 39PQ

(a)

To determine

The vector A→ in component form.

Answer 8

(a)

Expert Solution

Answer to Problem 39PQ

The vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Write the expression to find the component form of any vector.

A→=xi^+yj^+zk^

Here, x is the x component of the vector, y is the y component of the vector and z is the z component of the vector.

Conclusion:

Substitute 15.0 m for x, −6.00 m for y and −3.00 m for z in the above equation.

A→=(15.0 m)i^+(−6.00 m)j^+(−3.00 m)k^=(15.0i^−6.00j^−3.00k^) m

Therefore, the vector A→ in component form is A→=(15.0i^−6.00j^−3.00k^) m_.

Answer 13

(b)

To determine

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→.

(b)

Expert Solution

Answer to Problem 39PQ

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Explanation of Solution

Write the expression to find the vector B→.

B→=13A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

B→=13((15.0i^−6.00j^−3.00k^) m)=(5.0i^−2.00j^−1.00k^) m

Therefore, the vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Answer 14

(b)

To determine

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→.

Answer 15

(b)

Expert Solution

Answer to Problem 39PQ

The vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Write the expression to find the vector B→.

B→=13A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

B→=13((15.0i^−6.00j^−3.00k^) m)=(5.0i^−2.00j^−1.00k^) m

Therefore, the vector B→ in component form having one-third the length of vector A→ but in the same direction of the vector A→ is B→=(5.00i^−2.00j^−1.00k^) m_.

Answer 20

(c)

To determine

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→.

(c)

Expert Solution

Answer to Problem 39PQ

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Explanation of Solution

Write the expression to find the vector C→.

C→=−3A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

C→=−3((15.0i^−6.00j^−3.00k^) m)=(−45.00i^+18.0j^+9.00k^) m

Therefore, the vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Answer 21

(c)

To determine

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→.

Answer 22

(c)

Expert Solution

Answer to Problem 39PQ

The vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Write the expression to find the vector C→.

C→=−3A→

Conclusion:

Substitute (15.0i^−6.00j^−3.00k^) m for A→ in the above equation.

C→=−3((15.0i^−6.00j^−3.00k^) m)=(−45.00i^+18.0j^+9.00k^) m

Therefore, the vector C→ in component form having thrice the length of vector A→ but in the opposite direction of the vector A→ is C→=(−45.00i^+18.0j^+9.00k^) m_.