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In Exercises 28-31, find projuvandprojvu.

u=1,4,v=2,-3

Short Answer

Expert verified

The values areprojuv=-10171,4andprojvu=-10132,-3.

Step by step solution

01

Step 1. Given information.

The given vectors are:

u=1,4,v=2,-3

02

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

projuv=u·vu2uu=1,4,v=2,-3u·v=12+4-3=2-12=-10u=12+42=1+16=17

Then

projuv=u·vu2u=-101721,4=-10171,4

Therefore,projuv=-10171,4.

03

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

projvu=u·vv2vu=1,4,v=2,-3v=22+-32=4+9=13

Then,

projvu=u·vv2v=-101322,-3=-10132,-3

Therefore,projvu=u·vv2v=-10132,-3.

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