### Home > PC > Chapter 10 > Lesson 10.1.4 > Problem10-56

10-56.

What is the value of a given $\textbf{v} = \langle 3,6 a \rangle$ and $\textbf{w} = \langle - 16,2 a \rangle$ if $\textbf{v}$ and $\textbf{w}$ are orthogonal?

If two vectors are orthogonal, then their dot product is $0$.

$\textbf{u} · \textbf{v} = 3\left(−16\right) + \left(6a\right)\left(2a\right)$

Now set the dot product $= 0$ and solve for $a$.