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Let = (1,2) and 7=(3, a) be two vectors in R². (a) For which value of a the two vectors an are parallel? For which value of a they are orthogonal to each other? (b) For which value(s) of a the two vectors an are linearly independent?

Let = (1,2) and 7=(3, a) be two vectors in R². (a) For which value of a the two vectors an are parallel? For which value of a they are orthogonal to each other? (b) For which value(s) of a the two vectors an are linearly independent?

Advanced Engineering Mathematics
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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1. Let (1,2) and 7: = (a) For which value of a the two vectors an are parallel? For which value of a they are orthogonal to each other? (b) For which value(s) of a the two vectors an 2. Consider the vectors (a) Is (b) Is = (3, a) be two vectors in R². Let = (1, 1, 1, 1) (1,2,3,0), = (0,1,2,3) and = (2,3,4,-3) a linear combination of a linear combination of are linearly independent? and ?? , and ?
Transcribed Image Text:1. Let (1,2) and 7: = (a) For which value of a the two vectors an are parallel? For which value of a they are orthogonal to each other? (b) For which value(s) of a the two vectors an 2. Consider the vectors (a) Is (b) Is = (3, a) be two vectors in R². Let = (1, 1, 1, 1) (1,2,3,0), = (0,1,2,3) and = (2,3,4,-3) a linear combination of a linear combination of are linearly independent? and ?? , and ?
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Vector is parallel to another iff one is constant multiple of other .example: u=kv

Orthogonal when their dot product is zero.

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