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  • Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 17.

Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 17.

Answers (1)

ANSWER:

  3

HINT:

 Use formula |\vec{a} \times \vec{b}|^{2}+(\vec{a} \vec{b})^{2}=|\vec{a}|^{2}|\vec{b}|^{2}

GIVEN:

 |\vec{a} \times \vec{b}|^{2}+(\vec{a} \vec{b})^{2}=144 \quad \& \quad|\vec{a}|=4

SOLUTION:

|\vec{a} \times \vec{b}|^{2}+(\vec{a} \vec{b})^{2}=144 \quad \& \quad|\vec{a}|=4

We have

\begin{aligned} |\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|^{2}+(\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}})^{2} &=|\overrightarrow{\mathrm{a}}|^{2}|\overrightarrow{\mathrm{b}}|^{2} \\ 144 &=(4)^{2}|\overrightarrow{\mathrm{b}}|^{2} \\ |\overrightarrow{\mathrm{b}}|^{2} &=\frac{144}{16} \\ |\overrightarrow{\mathrm{b}}|^{2} &=9 \\ \qquad|\overrightarrow{\mathrm{b}}| &=3 \end{aligned}

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