Answer
See explanation
Work Step by Step
The angle between two non zero vectors is:
$$\cos(\theta)=\frac{u\cdot v}{|u||v|}$$
Two vector are perpendicular if $\theta=\frac{\pi}{2}$ so:
$$\cos(\frac{\pi}{2})=\frac{u\cdot v}{|u||v|}$$
$$0=\frac{u\cdot v}{|u||v|}$$
$$0=u\cdot v$$
Using the definition of the dot product it follows:
$$0=ac+bd$$
Swap both sides:
$$ac+bd=0$$
