Define a vector of length 1 orthogonal to $\vec{v} = (-4 \qquad 3)^t$
I'm looking for the solution in terms of $\vec{a} = \binom{x}{y}$.
How do I go about it? I'm familiar with addition, subtraction and multiplication of vectors and scalars.
I tried to use the formula
$\vec{a} * \vec{b} = ||\vec{a}|| * ||\vec{b}|| * \cos{(\alpha)}$
but since the unknown vector is orthogonal to $\vec{v}$, $\cos{(90°)}$ becomes $0$, thus everything becomes $0$. I'm at a loss here.