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  • Please solve RD Sharma class 12 chapter Vector or Cross Product exercise 24.1 question 37 maths textbook solution

Please solve RD Sharma class 12 chapter Vector or Cross Product exercise 24.1 question 37 maths textbook solution

Answers (1)

Answer:

 4

Hint: To solve this we use |\vec{a} \times \vec{b}|,|\vec{a} \cdot \vec{b}| formula

Given: |\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=400

Solution:

\begin{aligned} &|\vec{a} \times \vec{b}|=|\vec{a}| \times|\vec{b}| \sin \theta \\\\ &|\vec{a} \cdot \vec{b}|=|\vec{a}| \times|\vec{b}| \cos \theta \\\\ &|\vec{a}|^{2}|\vec{b}|^{2} \sin ^{2} \theta+|\vec{a}|^{2}|\vec{b}|^{2} \cos ^{2} \theta=400 \end{aligned}

\begin{aligned} &|\vec{a}|^{2}|\vec{b}|^{2}\left(\sin ^{2} \theta+\cos ^{2} \theta\right)=400 \\\\ &|\vec{a}|^{2}|\vec{b}|^{2}=400 \\\\ &|\vec{b}|^{2}=\frac{400}{|\vec{a}|^{2}}=\frac{400}{5^{2}}=\frac{400}{25} \end{aligned}

\begin{aligned} &|\vec{b}|^{2}=16 \\\\ &|\vec{b}|=4 \end{aligned}

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