#### Please solve RD Sharma class 12 chapter Vector or Cross Product exercise 24.1 question 13 maths textbook solution

Hint               : To solve this formula  $\vec{a} \cdot \vec{b} \text { and }|\vec{a} \times \vec{b}|$

Given            : $|\vec{a}|=13 \quad ;|\vec{b}|=5$

$\vec{a} \cdot \vec{b}=60$

Solution       :  $\vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos \theta$

\begin{aligned} &60=(13)(5) \cos \theta \\\\ &\cos \theta=\frac{60}{13 \times 5}=\frac{12}{13} \end{aligned}

\begin{aligned} &\cos ^{2} \theta+\sin ^{2} \theta=1 \\\\ &\sin \theta=\sqrt{1+\cos ^{2} \theta} \\\\ &=\sqrt{1-\left(\frac{12}{13}\right)^{2}} \end{aligned}

\begin{aligned} &=\sqrt{1-\frac{144}{169}} \\\\ &=\sqrt{\frac{169-144}{169}} \\\\ &=\sqrt{\frac{25}{169}} \end{aligned}

\begin{aligned} &=\frac{5}{13} \\\\ &|\vec{a} \times \vec{b}|=|| \vec{a}|| \vec{b}|\sin \theta| \\\\ &=13 \times 5 \times \frac{5}{13} \\\\ &=25 \end{aligned}

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