Question

What is the cross product of two parallel vectors?

Answer 1

1. The cross product between two vectors can be written as $\overrightarrow{A}\times \overrightarrow{B}=AB\sin \theta .\overbrace{n}$ where $\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors, $\theta$ is the angle between the two vectors and $\hat{n}$ is the unit vector in the perpendicular direction to both $\overrightarrow{A}$ and $\overrightarrow{B}$
2. If two vectors are in the same direction but in different magnitude then they are called parallel vectors.
3. Thus, for parallel vectors the angle between them is zero.
4. Hence, $$\begin{gathered} \overrightarrow{A}\times \overrightarrow{B}=AB\sin 0 \\ \overrightarrow{A}\times \overrightarrow{B}=0 \end{gathered}$$

Therefore, the cross product between two parallel vectors is zero.