Exercise 6

The definition of the dot product contains the cosine of the angle between the two vecotors:

\[\vec{A} \cdot \vec{B} = \left|\vec{A}\right| \left|\vec{B}\right| \cos \varphi\]

If the two vectors are orthogonal, the angle between them is \(90^\circ\).

Since \(\cos 90^\circ = 0\), the value of the dot product is zero.