What must be the dot product of two vectors that are perpendicular to each other?Group of answer choiceszeromaximumminimumnegative

The dot product of two vectors is defined mathematically as:

$\mathbf{A} \cdot \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \cos(\theta)$

where $|\mathbf{A}|$ and $|\mathbf{B}|$ are the magnitudes of the vectors, and $\theta$ is the angle between them.

Analysis:

1. If two vectors are perpendicular, the angle $\theta$ between them is $90^\circ$.
2. Using the cosine function, we know $\cos(90^\circ) = 0$.
3. Therefore, substituting that into the dot product formula gives: $\mathbf{A} \cdot \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \cdot 0 = 0$

Summary:

The dot product of two vectors that are perpendicular to each other is always zero.

Final Answer:

Zero