Unit vectors orthogonal to L

Question

I have a line $L$ in $\mathbb{R}^2$ that passes through two points:

$u = [9;7]$

$v = [1;-5]$

How do I find all unit vectors orthogonal to $L$?

I know:

$[x;y] * [8;12] = 0$

and

$x^2 + y^2 = 1$

But how do I finish off solving? Thanks

Answer 1

You have the equation $$ 8 x + 12 y =0 \iff x=-\frac{3}{2} y$$ using this you should be able to calculate the rest.