Question

Find two vectors v1 and v2 and whose sum is(3,0,2) , where v1 is parallel to(-4,-2,-4) while v2 is perpendicular to (-4,-2,-4)

Answer 1

Denote U=(-4,-2,-4) and
So here goes Let us suppose - to simplify, that the first vector is U + c*U

Answer 2

And denote the vector (3,0,2) by F

Answer 3

Now Let D = F - U

Answer 4

D being the second vector?

Answer 5

D is a vector in 3Dim linear space

Answer 6

D is the DIFFRENCE between Final and U

Answer 7

Okay, and it is also the vector perpendicular to U+c*U ?

Answer 8

No, it is the first step to compute D.
The second step - is to separate D into One part perpendicular to U and ANOTHER part parallel to U

Answer 9

How does one do that? Well , R u familiar with projection on a linear sub-space ?

Answer 10

Ohhhh, yes, okay okay! I didn't think it was a projection problem.
Alright, thank you!

Answer 11

Medal is due

Answer 12

Pls close the question.

Answer 13

The parallel part will be that little addition c*U