Hi, I'm struggling with this problem:

For

[-4, 1, 10]^T and

[−12, −6, 8]^T find the vectors

and

such that:

(i)

is parallel to

(ii)

is orthogonal to

(iii)

I figured I should firstly try and find u2 by (ii), and then after I found that I would be able to use (iii) to get u1. This approach didn't work out too well for me, heh. Basically I tried to set it up with dot product, and solve for u2:

Didn't work out, just ended up with something like: -12a - 6b + 8c = 0

Where a, b, c are the numbers in u2.

From there I couldn't see what more I could do to find a, b, c. Basically, I don't really know how to approach this problem

.

Anyone mind helping out a math newbie? Thanks in advance!