Student Workbook for Physics for Scientists and Engineers: A Strategic Approach, Vol 1. (Chs 1-21)
4th Edition
ISBN: 9780134110646
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Textbook Question
Chapter 3, Problem 4CQ
Is it possible to add a scalar to a vector? If so, demonstrate. If not, explain why not.
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Students have asked these similar questions
Given two vectors A = - 2.00 + 3.00ĵ + 4.00 k and B = 3.00 î+ 1.00 – 3.00 k, (a) find the
magnitude of each vector; (b) use unit vectors to write an expression for the vector difference A
B. Is this the same as the magnitude of B
(c) find the magnitude of the vector difference A
Explain.
B; and
A?
A scalar c = -0.75 is multiplied to the vector A. Which of the following
happens?
O The vector shrinks and has its direction reversed.
O The vector shrinks but maintains its direction.
O The vector elongates and has its direction reversed.
O The vector elongates but maintains its direction.
None of the given choices.
The Scalar Product
The vectors A andB are given by A = 31 + 1j and B = -1î + 1j.
(a) Determine the scalar product A - B.
SOLUTION
Conceptualize There is no physical system to imagine here. Rather, it is purely a mathematical exercise involving two (vectors
Categorize Because we have a definition for the scalar product, we categorize this example as a substitution vy problem.
Substitute the specific vector expressions for A and B:
A-B = (31 + 1j) - (-1î + 1j)
= [3i - (-1)i - [31 - 15 - 13 - (-1) + [1j - 15]
The same result is obtained when we use the equation A -B = AB, + A8, + A,B, directly, where A, = 3, A, = 1, B, = -1 and 8, = 1.
(b) Find the angle e between A and B.
SOLUTION
Evaluate the magnitudes of A and B using the Pythagorean theorem:
A = VA,? + A, =
B = V82 + B 2 =
Use the equation A - B = AB cos(e) and the result from part (a) to find the angle (in degrees).
cos(e) =
AB
EXERCISE
As a particle moves from the origin to (7i + 5j) m, it is acted upon by a force given by (7î +…
Chapter 3 Solutions
Student Workbook for Physics for Scientists and Engineers: A Strategic Approach, Vol 1. (Chs 1-21)
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Ch. 3 - Trace the vectors in FIGURE EX3.2 onto your paper....Ch. 3 - a. What are the x- and v-components of vector E...Ch. 3 - A velocity vector 40° below the positive x-axis...Ch. 3 - A position vector in the first quadrant has an...Ch. 3 - Draw each of the following vectors. Then find its...Ch. 3 - Draw each of the following vectors. Then find its...Ch. 3 - Let C = (3.15 m, 15° above the negative x-axis)...Ch. 3 - A runner is training for an upcoming marathon by...Ch. 3 - Draw each of the following vectors, label an angle...Ch. 3 - Draw each of the following vectors, label an angle...Ch. 3 - Let a. Write Vector Cin component form. b. Draw a...Ch. 3 - a. Write vector Cin component form. b. Draw a...Ch. 3 - a. Write vector Din component form. b. Draw a...Ch. 3 - Let A = 4î - 2j, B = -3î + 5j, and E = 2 A + 3 B...Ch. 3 - Let A = 41 - 2j, B = -3î + 5j, and F = A -4 B . a....Ch. 3 - 17. Let = 2î + 3? and = 2î — 2?. Find the...Ch. 3 - Prob. 18EAPCh. 3 - 19. What are the x– and y- components of the...Ch. 3 - 20. For the three vectors shown Figure EX3.20, + +...Ch. 3 - Prob. 21EAPCh. 3 - 22. Let = (3.0 m, 20° south of east), = (2.0 m,...Ch. 3 - The position of a particle as a function of time...Ch. 3 - a. What is the angle between vectors E and F in...Ch. 3 - FIGURE P3.25 shows vectors A and B . Find vector C...Ch. 3 - Prob. 26EAPCh. 3 - Prob. 27EAPCh. 3 - Prob. 28EAPCh. 3 - The minute hand on a watch is 2.0 cm in length....Ch. 3 - Prob. 30EAPCh. 3 - Ruth sets out to visit her friend Ward, who lives...Ch. 3 - A cannon tilted upward at 30° fires a cannonball...Ch. 3 - Prob. 33EAPCh. 3 - Prob. 34EAPCh. 3 - A pine cone falls straight down from a pine tree...Ch. 3 - Prob. 36EAPCh. 3 - Prob. 37EAPCh. 3 - Your neighbor Paul has rented a truck with a...Ch. 3 - Tom is climbing a 3.0-m-long ladder that leans...Ch. 3 - The treasure map in FIGURE P3.40 gives the...Ch. 3 - The bacterium E. coli is a single-cell organism...Ch. 3 - A flock of ducks is trying to migrate south for...Ch. 3 - FIGURE P3.43 shows three ropes tied together in a...Ch. 3 - I Four forces are exerted on the object shown in...Ch. 3 - FIGURE P3.45 shows four electric charges located...
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- Lei B = 5.00 m at 60.0. Let the vector C have the same magnitude as A and a direction angle greater than that of A by 25.0. Let A B = 30.0 m2 and B C = 35.0 m2. Find the magnitude and direction of A.arrow_forwardWhat is the y component of the vector (3i8k) m/s? (a) 3 m/s (b) 8 m/s (c) 0 (d) 8 m/s (e) none of those answersarrow_forwardFind the scalar components of three-dimensional vectors G and H in the following figure and write the vectors in vector component form in terms of the unit vectors of the axes.arrow_forward
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