Question

take (v=langle - 10,-5
angle). write out (v_{perp}).

Explanation:

Step1: Recall perpendicular vector formula

For a two - dimensional vector $\vec{V}=(a,b)$, a vector $\vec{V}_{\perp}=(x,y)$ perpendicular to it satisfies $a x + b y=0$. One way to find a perpendicular vector is to swap the components and change the sign of one of them.
Let $\vec{V}=(- 10,-5)$. A vector perpendicular to it can be obtained by swapping the components and changing the sign of one of them.

Step2: Calculate the perpendicular vector

If we swap the components of $\vec{V}=(-10,-5)$ and change the sign of the first component, we get $\vec{V}_{\perp}=( - 5,10)$. Another possible perpendicular vector is $(5, - 10)$ (by changing the sign of the second component after swapping). Usually, we can choose one of them. Let's choose $\vec{V}_{\perp}=(5,-10)$.

Answer:

$(5,-10)$