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In Exercises 24-27, find compuv,projuv and the component of v orthogonal tou.

u=2,0,-5,v=-3,7,-1

Short Answer

Expert verified

The values are compuv=-129,projuv=-1292,0,-5 and the component of v orthogonal tou is-8529,7,-329.

Step by step solution

01

Step 1. Given information.

The given vectors are:

u=2,0,-5andv=-3,7,-1

02

Step 2. Find the component of the projection of v onto u.

compuv=u·vuu=2,0,-5andv=-3,7,-1u·v=2-3+07+-5-1=-6+0+5=-1u=22+02+-52=4+0+25=29

Then,

compuv=u·vu=-129

Therefore, localid="1649675490199" compuv=-129.

03

Step 3. Find the vector projection of v onto u.

projuv=u·vu2u=-12922,0,-5=-1292,0,-5

Therefore, the vector projection of v onto uis-1292,0,-5.

04

Step 4. Find the component of v orthogonal to u.

The component of v orthogonal tou isv-projuv.

v-projuv=-3,7,-1--1292,0,-5=-3,7,-1+1292,0,-5=-3+229,7+0,-1,-529=-8529,7,-329

Therefore, the component of v orthogonal to u is-8529,7,-329.

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