1. Use the vectors drawn in the diagram below to complete the following exercises. E C D E CH resulted TORNSTEUNEN 5 À (all vectors in this diagram lie in the plane of the board) a) Write an expression to describe the dot product between vectors B and D. b) Write an expression to describe the magnitude of the cross product between vectors A and D. c) Draw a new vector, named G, that would result in a dot product less than zero when dotted with vector E. d) Draw the direction of a new vector, named , that when crossed with vector B (HxB) would result in a cross product that points out of the board.
1. Use the vectors drawn in the diagram below to complete the following exercises. E C D E CH resulted TORNSTEUNEN 5 À (all vectors in this diagram lie in the plane of the board) a) Write an expression to describe the dot product between vectors B and D. b) Write an expression to describe the magnitude of the cross product between vectors A and D. c) Draw a new vector, named G, that would result in a dot product less than zero when dotted with vector E. d) Draw the direction of a new vector, named , that when crossed with vector B (HxB) would result in a cross product that points out of the board.
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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e) Name two vectors in the diagram that when dotted, would generate a dot product of 0. Explain your reasoning.
f) Name two vectors in the diagram that when crossed, would generate a cross product of 0. Explain your reasoning.
g) If \(|\vec{C}| = 5.2 \, \text{m}, \, |\vec{D}| = 3.5 \, \text{m},\) and \(\vec{C} \cdot \vec{D} = 15.76 \, \text{m}^2\) then determine the angle \(\psi\).

Transcribed Image Text:**Exercise: Vector Operations**
**Instructions:** Use the vectors drawn in the diagram below to complete the following exercises.
**Diagram Explanation:**
- The diagram displays five vectors labeled \( \vec{A}, \vec{B}, \vec{C}, \vec{D}, \vec{E} \).
- The angles between vectors are marked as \( \alpha, \beta, \delta, \epsilon, \phi, \psi \).
- All vectors lie in the plane of the board.
**Exercises:**
a) Write an expression to describe the dot product between vectors \( \vec{B} \) and \( \vec{D} \).
b) Write an expression to describe the magnitude of the cross product between vectors \( \vec{A} \) and \( \vec{D} \).
c) Draw a new vector, named \( \vec{G} \), that would result in a dot product less than zero when dotted with vector \( \vec{E} \).
d) Draw the direction of a new vector, named \( \vec{H} \), that when crossed with vector \( \vec{B} \) (i.e., \( \vec{H} \times \vec{B} \)) would result in a cross product that points out of the board.
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