Question

True or False $\left|\left|u\times v\right|\right|=\left|\left|u\right|\right|\left|\left|v\right|\right|\cos \theta ,$where $\theta$is the angle between $u$and $v$.

Short answer

The given statement is false.

Step-by-step solution

Step 1 Definition for cross product:

Cross product of two vectors is the method of multiplication of two vectors. A cross product is denoted by the multiplication sign$\left(\times \right)$ between two vectors. It is a binary vector operation, defined in a three-dimensional system. The cross product of two vectors is the third vector that is perpendicular to the two original vectors.

Step 2 Reason for the given statement being false:  

It is false that, $\left|\left|u\times v\right|\right|=\left|\left|u\right|\right|\left|\left|v\right|\right|\cos \theta$, where $\theta$is the angle between $u$and $v$. Because, the geometric properties of the cross product states that $\left|\left|u\times v\right|\right|=\left|\left|u\right|\right|\left|\left|v\right|\right|\sin \theta$.