Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle between A and B b) Scalar projection of A on B Vector projection of B on A d) Area of the parallelogram whose sides are specified by A %3D and B
Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle between A and B b) Scalar projection of A on B Vector projection of B on A d) Area of the parallelogram whose sides are specified by A %3D and B
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q1. Given three vectors \( \mathbf{A} = -a_x + 2a_y + 3a_z \), \( \mathbf{B} = 3a_x + 4a_y + 5a_z \), and \( \mathbf{C} = 2a_x - 2a_y + 7a_z \), compute:
a) Angle between \( \mathbf{A} \) and \( \mathbf{B} \)
b) Scalar projection of \( \mathbf{A} \) on \( \mathbf{B} \)
c) Vector projection of \( \mathbf{B} \) on \( \mathbf{A} \)
d) Area of the parallelogram whose sides are specified by \( \mathbf{A} \) and \( \mathbf{B} \)
Q2. Given points \( P(4, -5, 4) \), \( Q(-2, 3, 2) \) find:
a) Draw position vector of point \( P \) and \( Q \)
b) Draw and write the distance from \( P \) to \( Q \)
c) A unit vector directed from \( P \) to \( Q \)
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