1. Use the vectors drawn in the diagram below to complete the following exercises. D E Ĉ 4 16 α B Ф B A (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 Ď. 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. 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 |C| = 5.2 m, |D| = 3.5 m, and C · D = 15.76 m² then determine the . angle .
1. Use the vectors drawn in the diagram below to complete the following exercises. D E Ĉ 4 16 α B Ф B A (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 Ď. 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. 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 |C| = 5.2 m, |D| = 3.5 m, and C · D = 15.76 m² then determine the . angle .
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Complete only parts d-g.
*(All vectors in this diagram lie in the plane of the board)*
- Vector \(\vec{A}\) is pointing horizontally to the right.
- Vector \(\vec{B}\) is pointing diagonally downward.
- Vector \(\vec{C}\) is pointing horizontally to the left.
- Vector \(\vec{D}\) is pointing vertically upward.
- Vector \(\vec{E}\) is pointing vertically upward.
Angles:
- \(\alpha\) is between \(\vec{C}\) and \(\vec{B}\)
- \(\beta\) is between \(\vec{B}\) and the vertical axis
- \(\delta\) is between \(\vec{A}\) and \(\vec{D}\)
- \(\epsilon\) is between \(\vec{D}\) and the vertical axis
- \(\psi\) is between \(\vec{C}\) and \(\vec{D}\)
- \(\Phi\) is the angle above the horizontal (\(\vec{A}\) axis)
**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 \(\vec{B}\) (\(\vec{H} \times \vec{B}\)) would result in a cross product that points out of the board.
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 \, m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbac5240b-2cb0-46ee-b04c-8db0831d9625%2F7a80001b-4c2a-42df-8b2d-87f4bc30dc7e%2Fls1psnc_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Vector Exercises with Dot and Cross Products**
**Instructions:**
1. **Use the vectors drawn in the diagram below to complete the following exercises.**
*(All vectors in this diagram lie in the plane of the board)*
- Vector \(\vec{A}\) is pointing horizontally to the right.
- Vector \(\vec{B}\) is pointing diagonally downward.
- Vector \(\vec{C}\) is pointing horizontally to the left.
- Vector \(\vec{D}\) is pointing vertically upward.
- Vector \(\vec{E}\) is pointing vertically upward.
Angles:
- \(\alpha\) is between \(\vec{C}\) and \(\vec{B}\)
- \(\beta\) is between \(\vec{B}\) and the vertical axis
- \(\delta\) is between \(\vec{A}\) and \(\vec{D}\)
- \(\epsilon\) is between \(\vec{D}\) and the vertical axis
- \(\psi\) is between \(\vec{C}\) and \(\vec{D}\)
- \(\Phi\) is the angle above the horizontal (\(\vec{A}\) axis)
**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 \(\vec{B}\) (\(\vec{H} \times \vec{B}\)) would result in a cross product that points out of the board.
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 \, m
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