Given two vectors p = (-3, -4, -3) and q = (4, -3, 3), find such vectors a and b that a+b= q; ais parallel to p; and b is orthogonal to p. HINT. You can either use the knowledge that you already have or do the following: First, notice that the parallelity of a to p implies that a = tp for some real number t. Second, take the dot product of both parts of the equation q = tp + b with the vector p. A certain summand (which?) will produce zero, and this will allow you to find t. Once you've found t, it will be easy to find first a and then b. Vector a: (000) Vector b: (000)
Given two vectors p = (-3, -4, -3) and q = (4, -3, 3), find such vectors a and b that a+b= q; ais parallel to p; and b is orthogonal to p. HINT. You can either use the knowledge that you already have or do the following: First, notice that the parallelity of a to p implies that a = tp for some real number t. Second, take the dot product of both parts of the equation q = tp + b with the vector p. A certain summand (which?) will produce zero, and this will allow you to find t. Once you've found t, it will be easy to find first a and then b. Vector a: (000) Vector b: (000)
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:Given two vectors p = (-3, -4, -3) and q = (4, -3, 3), find such vectors a and b that a+b= q; ais parallel to p; and b is orthogonal to p.
HINT. You can either use the knowledge that you already have or do the following:
First, notice that the parallelity of a to p implies that a = tp for some real number t.
Second, take the dot product of both parts of the equation q = tp + b with the vector p. A certain summand (which?) will produce zero, and this will allow you
to find t. Once you've found t, it will be easy to find first a and then b.
Vector a:
Vector b:
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