Vector problem involving orthogonal
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
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!