Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 9, Problem 11PQ
To determine
The dot product of the vectors
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With the given three vector A, B, C. Determine the magnitude of the dot product of vectors AxC and CxB
A= 2i - 3j + 4k
B= -3i - 6j + 5k
C= 4i + 2j
Using the definition of dot product:
Ax B= (A,B₂ - A₂By)i + (A₂Bx − AxB₂)j + (AxBy - Ay Bx)k
Find the cross product Ax B the following vectors:
(a)
U
A = 11 + 3) + 0k
B = 3î + 1ĵ + 0k
A = 11 - 3j+2k
B = -31 + 1ĵ+ 0k
(b)
(d)
A = 1î + 1ĵ + Ok
B = 2î - 3j+0k
A = 21-5j-1k
B = 3î + 1ĵ+ 3k
Given two vectors A⃗ = 4.20 i^+ 7.60 j^ and B⃗ = 5.70 i^− 2.40 j^ , find the scalar product of the two vectors A⃗ and B⃗ .
Find the angle between these two vectors.
Chapter 9 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 9.4 - In the three cases shown in Figure 9.11, a force...Ch. 9.6 - Prob. 9.2CECh. 9.6 - Prob. 9.3CECh. 9.7 - Prob. 9.4CECh. 9.7 - Prob. 9.5CECh. 9.9 - Prob. 9.6CECh. 9 - Pick an isolated system for the following...Ch. 9 - Prob. 2PQCh. 9 - Prob. 3PQCh. 9 - Prob. 4PQ
Ch. 9 - Prob. 5PQCh. 9 - Prob. 6PQCh. 9 - Prob. 7PQCh. 9 - A 537-kg trailer is hitched to a truck. Find the...Ch. 9 - Prob. 9PQCh. 9 - A helicopter rescues a trapped person of mass m =...Ch. 9 - Prob. 11PQCh. 9 - An object is subject to a force F=(512i134j) N...Ch. 9 - Prob. 13PQCh. 9 - Prob. 14PQCh. 9 - Prob. 15PQCh. 9 - Prob. 16PQCh. 9 - Prob. 17PQCh. 9 - Prob. 18PQCh. 9 - Prob. 19PQCh. 9 - Prob. 20PQCh. 9 - Prob. 21PQCh. 9 - Prob. 22PQCh. 9 - A constant force of magnitude 4.75 N is exerted on...Ch. 9 - In three cases, a force acts on a particle, and...Ch. 9 - An object of mass m = 5.8 kg moves under the...Ch. 9 - A nonconstant force is exerted on a particle as it...Ch. 9 - Prob. 27PQCh. 9 - Prob. 28PQCh. 9 - Prob. 29PQCh. 9 - A particle moves in the xy plane (Fig. P9.30) from...Ch. 9 - A small object is attached to two springs of the...Ch. 9 - Prob. 32PQCh. 9 - Prob. 33PQCh. 9 - Prob. 34PQCh. 9 - Prob. 35PQCh. 9 - Prob. 36PQCh. 9 - Prob. 37PQCh. 9 - Prob. 38PQCh. 9 - A shopper weighs 3.00 kg of apples on a...Ch. 9 - Prob. 40PQCh. 9 - Prob. 41PQCh. 9 - Prob. 42PQCh. 9 - Prob. 43PQCh. 9 - Prob. 44PQCh. 9 - Prob. 45PQCh. 9 - Prob. 46PQCh. 9 - Prob. 47PQCh. 9 - Prob. 48PQCh. 9 - Prob. 49PQCh. 9 - A small 0.65-kg box is launched from rest by a...Ch. 9 - A small 0.65-kg box is launched from rest by a...Ch. 9 - A horizontal spring with force constant k = 625...Ch. 9 - A box of mass m = 2.00 kg is dropped from rest...Ch. 9 - Prob. 54PQCh. 9 - Return to Example 9.9 and use the result to find...Ch. 9 - Prob. 56PQCh. 9 - Crall and Whipple design a loop-the-loop track for...Ch. 9 - Prob. 58PQCh. 9 - Calculate the force required to pull a stuffed toy...Ch. 9 - Prob. 60PQCh. 9 - Prob. 61PQCh. 9 - Prob. 62PQCh. 9 - An elevator motor moves a car with six people...Ch. 9 - Prob. 64PQCh. 9 - Figure P9.65A shows a crate attached to a rope...Ch. 9 - Prob. 66PQCh. 9 - Prob. 67PQCh. 9 - Prob. 68PQCh. 9 - Prob. 69PQCh. 9 - Prob. 70PQCh. 9 - Prob. 71PQCh. 9 - Estimate the power required for a boxer to jump...Ch. 9 - Prob. 73PQCh. 9 - Prob. 74PQCh. 9 - Prob. 75PQCh. 9 - Prob. 76PQCh. 9 - Prob. 77PQCh. 9 - Prob. 78PQCh. 9 - Prob. 79PQCh. 9 - A block of mass m = 0.250 kg is pressed against a...Ch. 9 - On a movie set, an alien spacecraft is to be...Ch. 9 - Prob. 82PQCh. 9 - A spring-loaded toy gun is aimed vertically and...Ch. 9 - Prob. 84PQCh. 9 - The motion of a box of mass m = 2.00 kg along the...Ch. 9 - Prob. 86PQCh. 9 - Prob. 87PQCh. 9 - Prob. 88PQ
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- Find the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m and B=(-2.0i+3.0j+2.0K)m .arrow_forwardWhich of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors? (a) AB is larger than AB. (b) AB is smaller than AB. (c) AB could be larger or smaller than AB, depending on the angle between the vectors. (d) AB could be equal to AB.arrow_forwardGiven M = î + 5 j - 6 k and N = 2 î - 2 j - 3 k, calculate the vector product M × N. Î + +arrow_forward
- If vector A = 2 i+2j° and vector B = 6 i +8j^, then 8 A+2 B = O a. 28 i - 32 j O b. 28 i +0 j O c. 28 i +32 j O d. 4 i +32 j Scalar or dot product of vectors 9 i+ 6 j+ -4 k and 1 i+3j+0k is: Answer:arrow_forwardUse the definition of scalar product, ?→⋅?→�→⋅�→ = ab cos θ, and the fact that ?→⋅?→�→⋅�→ = axbx + ayby + azbz to calculate the angle between the two vectors given by ?→=6.0?̂ +6.0?̂+6.0?̂�→=6.0�̂+6.0�̂+6.0�̂ and ?→=2.0?̂ +2.0?̂+3.0?̂�→=2.0�̂+2.0�̂+3.0�̂.arrow_forwardScalars and vectors: Vector A has a magnitude of 9.0 and Vector B has a magnitude of 3.0. If the vectors are at an angle of 30.0º, what is the magnitude of the cross product A x B? Here are the choices: 13.5 16.2 23.4 27.0arrow_forward
- Use the definition of scalar product, a = ab cos 0, and the fact that a . the two vectors given by a = 3.01 +3.0 + 3.0k and b Number i Units = axbx + ab + a₂b₂ to calculate the angle between 4.0î + 9.0ĵ + 7.0k. =arrow_forwardFind for the Cross Product of the following pairs of vectors 1. A=4i-5j +8k, B = -2i+3j+3k 2. C = -6i+4j+7k, D=4i-j+5k 3. E= -i-5j + 2k, F = 8i+2j-6karrow_forwardUsing the definition of dot product: A B = ABCOS (0AB) = AxBx + Ay By + A₂B₂ Find the angle between the following vectors: (c) A = 1î + 3j+0k B = 3î + 1) + Ok A = 1î - 3j + 2k B = -31 + 1) + 0k (b) (d) A = 1î + 1ĵ + Ok B = 21-3j+0k A = 21-5j-1k B = 3î + 11 + 3karrow_forward
- You are given 3 vectors: p = j - 3k, q = -2i - j - 3k and r = 4i + j + 3k. You are informed that these three vectors are Cartesian unit vectors.What is the vector product of q x r?arrow_forwardGiven the vectors A = (8i + 4j - 2k) N B = (2j + 6k) m C = (3i - 2j + 4k) m Calculate the following: (a) the dot product of vectors A and B; (b) the projected component of B in the direction of C; (c) the angle between B and C.arrow_forwardTwo vectors in Cartesian coordinates have components A=(2,3,2) and B=(4,-1,7). What is the dot product of vector A with vector B? A•B=arrow_forward
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