Find a vector's component given that the vector is perpendicular to another vector

Question

What value of $a$ makes vector ${\bf u} = (a,1)$ perpendicular to ${\bf v} = (3,2)$?

Answer 1

If $\vec u$ and $\vec v$ are perpendicular, then $\vec u\cdot\vec v=0$.

Thus $(a,1)\cdot(3,2)=3a+2=0$.

Can you take it from here?

Answer 2

This may help you visualize the problem: