Give a unit vector perpendicular to vector $v=2i+3j$.

Question

Solution is "multiples of $3i-2j$". How is this answer reached?

Answer 1

Hint: $u = xi +yj \perp yi -xj$. You can take $v = \dfrac{yi-xj}{\sqrt{x^2+y^2}}$, and use $x = 2$, and $y = 3$. Then: $u \perp v$, and $||v|| = 1$