(a) Show that if v = ai + bj is a vector in 2-space, thenthe vectorsv1 = bi + a j and v2

Chapter 11, Problem 8

(choose chapter or problem)

(a) Show that if $v=a i+b j$ is a vector in 2 -space, then the vectors

$v_{1}=-b i+a j \text { and } v_{2}=b i-a j$ are both orthogonal to v.

(b) Use the result in part (a) to find two unit vectors that are orthogonal to the vector $v=3 i-2 j$. Sketch the vectors $v, v_{1}$, and $v_{2}$

Equation Transcription:

$v=ai+bj$

${v}_{1}=-bi+aj\ and\ {v}_{2}=bi-aj$

$v=3i-2j$

$v,{v}_{1}$

${v}_{2}$

Text Transcription:

v=ai+bj

v_1=-bi+aj and v_2=bi-aj

v=3i-2j

v,v_1

v_2

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