(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
Want to see more full solutions like this?
Chapter 9 Solutions
PRECALCULUS
- VelocitySuppose that in Exercise 55 the current is flowing at 1.2 mi/hr due south. In what direction should the swimmer head in order to arrive at a landing point due east of his starting point? VelocityA river flows due south at 3mi/h. A swimmer attempting to cross the river heads due east swimming at 2mi/h relative to the water. Find the true velocity of the swimmer as a vector.arrow_forwardWhat is the unit vector in the direction of v = < - 5 , - 1 > ?arrow_forwardAt an air show, a jet has a trajectory following the curve y = 3x². When the jet is at the point (5, 75), it has a speed of 550 km/h. Determine the velocity vector at this point. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer using component form or standard basis vectors.) velocity:arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,