Let u = (u1, u2, u3) v = (v1, v2, v3) and w = (w1, w2, w3) be non collinear vectors.
Find the scalar $\alpha$ so that u + $\alpha$ v is perpendicular to w.
I know that for a vector to be perpendicular to another, their dot product needs to be 0.
I get something like:
(u1 + $\alpha$ v1)(w1) = 0
(u2 + $\alpha$ v2)(w2) = 0
(u3 + $\alpha$ v3)(w3) = 0
My problem is that I don't know how to isolate the scalar in the formula.
In this exercise, the real values are u = (2,3,1) v = (0,2,3) and z = (4,3,3)
Any tips on how to solve this?