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

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

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Answer         : 25

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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