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10-29.

What is the value of $a$, given $\vec { \text v }= ⟨3, 6a⟩$ and $\vec { \text w }= ⟨−16, 2a⟩,$ if $\vec { \text v }$ and $\vec { \text w }$ are perpendicular?

If two vectors are perpendicular, then their dot product is $0$.
Or, their slopes are opposite reciprocals.

$\textbf{u} · \textbf{v} = 3(−16) + (6a)(2a) = 0$

OR $\frac{6a}{3}=-\frac{16}{2a}$