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

u=1,2,v=3,5

Short Answer

Expert verified

The values are compuv=135,projuv=1351,2 and the component of v orthogonal tou is25,-15.

Step by step solution

01

Step 1. Given information.

The given vectors are:

u=1,2andv=3,5

02

Step 2. Find compu v.

compuv=u·vuis the projection of vonto u.

u=1,2andv=3,5u·v=13+25=3+10=13u=12+22=1+4=5

then, localid="1649668447466" compuv=u·vuis:

localid="1649667564938" =135

03

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

projuv=u·vu2u=13521,2=1351,2

04

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

The component of v orthogonal tou isv-projuv.

v-projuv=3,5-1351,2=3,5-135,265=25,-15

Therefore, the component of v orthogonal to u is localid="1649668403950" 25,-15.

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