Question

If ${|\overrightarrow{a}\times \overrightarrow{b}|}^2+{|\overrightarrow{a}.\overrightarrow{b}|}^2=100and\left|\overrightarrow{a}\right|=5,$ then find the value of $\left|\overrightarrow{b}\right|$ is

• A. $25$
• B. $20$
• C. $10$
• D. $2$

Answer 1

The correct option is D $2$

We have,

$\begin{array}{c}{\left|\overrightarrow{a}\times \overrightarrow{b}\right|}^2+{\left|\overrightarrow{a}.\overrightarrow{b}\right|}^2=100\&\left|\overrightarrow{a}\right|=5\\ {\left|\overrightarrow{a}\right|}^2{\left|\overrightarrow{b}\right|}^2\left({\sin }^2\theta +{\cos }^2\theta \right)=100\\ {\left|\overrightarrow{a}\right|}^2{\left|\overrightarrow{b}\right|}^2=100\\ \left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|=\sqrt{100}=10\\ 5\left|\overrightarrow{b}\right|=10\\ \left|\overrightarrow{b}\right|=2\end{array}$

Hence, this is the answer.