Answer
Please refer to the step-by-step part.
Work Step by Step
By definition the dot product of $2$ vectors $ai+bj$ and $ci+dj$ is: $(ai+bj)(ci+dj)=ac+bd$.
Hence,
$0\cdot v\\
=(0i+0j)(ci+dj)\\
=0\cdot c+0\cdot d\\
=0.$
And this is what we wanted to prove.
