Two vectors are defined in component form below. Use them to answer the following questions. Note: ,ŷ, and 2 are Cartesian unit vectors. H = -59 +42 G = -52 +22 a) Determine A if A = H.G. b) IfJ = G H, then which of the following is true? (Choose all that are true.) Briefly explain your reasoning. i. A = -J ii. A = J c) Determine C in component form if C = H x G.
Two vectors are defined in component form below. Use them to answer the following questions. Note: ,ŷ, and 2 are Cartesian unit vectors. H = -59 +42 G = -52 +22 a) Determine A if A = H.G. b) IfJ = G H, then which of the following is true? (Choose all that are true.) Briefly explain your reasoning. i. A = -J ii. A = J c) Determine C in component form if C = H x G.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![Two vectors are defined in component form below. Use them to answer the following questions. Note: \( \hat{x}, \hat{y}, \) and \( \hat{z} \) are Cartesian unit vectors.
\[
\mathbf{G} = -5\hat{x} + 2\hat{z}
\]
\[
\mathbf{H} = -5\hat{y} + 4\hat{z}
\]
a) Determine \( A \) if \( A = \mathbf{H} \cdot \mathbf{G} \).
b) If \( J = \mathbf{G} \cdot \mathbf{H} \), then which of the following is true? (Choose all that are true.) Briefly explain your reasoning.
i. \( A = -J \)
ii. \( A = J \)
c) Determine \( \mathbf{C} \) in component form if \( \mathbf{C} = \mathbf{H} \times \mathbf{G} \).
d) If \( \mathbf{K} = \mathbf{G} \times \mathbf{H} \), then which of the following is true? (Choose all that are true.) Briefly explain your reasoning.
i. \( \mathbf{C} = -\mathbf{K} \)
ii. \( \mathbf{C} = \mathbf{K} \)
iii. \( \mathbf{C} \cdot \mathbf{K} = 0 \)
iv. \( \mathbf{C} \times \mathbf{K} = 0 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbac5240b-2cb0-46ee-b04c-8db0831d9625%2Fc2f6f2b1-e88f-415b-aa64-bcba48c0a920%2Fef91ova_processed.png&w=3840&q=75)
Transcribed Image Text:Two vectors are defined in component form below. Use them to answer the following questions. Note: \( \hat{x}, \hat{y}, \) and \( \hat{z} \) are Cartesian unit vectors.
\[
\mathbf{G} = -5\hat{x} + 2\hat{z}
\]
\[
\mathbf{H} = -5\hat{y} + 4\hat{z}
\]
a) Determine \( A \) if \( A = \mathbf{H} \cdot \mathbf{G} \).
b) If \( J = \mathbf{G} \cdot \mathbf{H} \), then which of the following is true? (Choose all that are true.) Briefly explain your reasoning.
i. \( A = -J \)
ii. \( A = J \)
c) Determine \( \mathbf{C} \) in component form if \( \mathbf{C} = \mathbf{H} \times \mathbf{G} \).
d) If \( \mathbf{K} = \mathbf{G} \times \mathbf{H} \), then which of the following is true? (Choose all that are true.) Briefly explain your reasoning.
i. \( \mathbf{C} = -\mathbf{K} \)
ii. \( \mathbf{C} = \mathbf{K} \)
iii. \( \mathbf{C} \cdot \mathbf{K} = 0 \)
iv. \( \mathbf{C} \times \mathbf{K} = 0 \)
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