Question

If |a x b|^2 + |a.b|^2 =400 and |a|=5 then find |b|

Answer 1

$\textbf{Given:}$

$|\vec{a}|=5\;\text{ and}$

$|\vec{a}{\times}\vec{b}|^2+(\vec{a}.\vec{b})^2=400$

$\text{Using,}$

$\boxed{\bf|\vec{a}{\times}\vec{b}|^2+(\vec{a}.\vec{b})^2=|\vec{a}|^2\,|\vec{b}|^2}$

$\text{we get}$

$|\vec{a}|^2\,|\vec{b}|^2=400$

$(5)^2\,|\vec{b}|^2=400$

$(25)|\vec{b}|^2=400$

$|\vec{b}|^2=16$

$|\vec{b}|=\sqrt{16}$

$\implies\boxed{\bf|\vec{b}|=4}$

Answer 2

Answer:

sorry I didn't the correct solution