
(a)
To explain: The
(a)

Explanation of Solution
A line segment with a particular direction running from initial point to terminal point is called a vector in the plane. A vector in the plane is denoted by
The vector
Where,
A vector represents a magnitude and a direction.
(b)
To find: The vector with initial point
(b)

Answer to Problem 1RCC
The vector with initial point
Explanation of Solution
Given:
The initial point is
Formula used:
The formula to calculate the vector
Calculation:
Substitute 2 for
Thus, the vector with initial point
(c)
The terminal point of the vector
(c)

Answer to Problem 1RCC
The terminal point of the vector
Explanation of Solution
Given:
The vector
Calculation:
Section (a):
The terminal point of
Substitute x for
Compare both sides,
Thus, the terminal point of the vector
Section (b):
Draw the graph of vector as shown below,
Figure (1)
Thus, Figure (1) shows various representations of the vector
(d)
The definition of magnitude of vector and the value of the vector
(d)

Explanation of Solution
Calculation:
The length of the line segment is called the magnitude of the vector and it is denoted by
The magnitude of the vector
Thus, magnitude of vector
(e)
The vectors
(e)

Explanation of Solution
Calculation:
A vector of length 1 is called a unit vector. The vectors
The vector
Thus, the vector
(f)
The direction
(f)

Explanation of Solution
Calculation:
The smallest positive angle in standard position formed by the positive x-axis and the vector
The vector
And
Where,
The vector
The graph for the above equation is,
Figure (2)
Thus, Figure (2) shows the graph of the coordinates of a vector in terms of length and direction.
(g)
To find: The vector
(g)

Answer to Problem 1RCC
The vector
Explanation of Solution
Given:
The length
Calculation:
The vector
And
Substitute 5 for
And
Substitute
Thus, the coordinates of the vector
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Chapter 9 Solutions
Student Solutions Manual for Stewart/Redlin/Watson's Precalculus: Mathematics for Calculus, 7th
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