Question

Are the vectors u=(2,3) and v=(-6, 4) orthogonal?

Answer 1

We need to find dot products of 2 vectors:

u·v = x1*x2 + y1*y2

u·v = 2*(-6) + 3*4 = -12 + 12 = 0

Another way to write dot product u·v = |u|*|v|*cos α.

Because the do product = 0, we can write

 |u|*|v|*cos α = 0.

That means cos α = 0, and thus α=90⁰, so vectors v and u  are orthogonal.