#### Please solve RD Sharma Class 12 Chapter 24 Vector or Cross Product Exercise Very Short Answer Question, question 7 Maths textbook solution.

$\left | a \right |^2\left | b \right |^2$

HINT:

Just drive the formulas for dot product and cross product and add them.

GIVEN:

SOLUTION:

\begin{aligned} &|\vec{a} \times \vec{b}|=|\vec{a}| \cdot|\vec{b}| \sin \theta \cdot \widehat{n} \\ &|\vec{a} \times \vec{b}|=|\vec{a}| \cdot|\vec{b}| \sin \theta .1 \quad(\because \widehat{n}=1, \text { as it is unit vector }) \\ &|\vec{a} \times \vec{b}|^{2}=|\vec{a}|^{2} \cdot|\vec{b}|^{2} \operatorname{\sin}^{2} \theta \ldots \ldots \ldots \ldots \ldots(1) \end{aligned}

\begin{aligned} &|\vec{a} \vec{b}|=|\vec{a}| \cdot|\vec{b}| \cos \theta \\ &|\vec{a} \vec{b}|^{2}=|\vec{a}|^{2} \cdot|\vec{b}|^{2} \operatorname{\cos}^{2} \theta . ............................(2)\\ &\text { Adding }(1) \&(2) \end{aligned}

\begin{aligned} |\vec{a} \times \vec{b}|^{2}+|\vec{a} \vec{b}|^{2} &=|a|^{2}|b|^{2}\left(\sin ^{2} \theta+\operatorname{Cos}^{2} \theta\right) \\ &=|a|^{2}|b|^{2}(1) \\ &=|a|^{2}|b|^{2} \end{aligned}