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  • Provide solution for RD sharma maths class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 8

Provide solution for RD sharma maths class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 8

Answers (1)

\frac{\pi}{3}

Hint:

Angle between \vec{a} and \vec{b}

Given:

If \vec{a}, \vec{b} are unit vector such that,\left | \vec{a}+ \vec{b} \right |=\sqrt{3}, then angle between \vec{a} and \vec{b} is

Solution:

\begin{aligned} &|\vec{a}+\vec{b}|=\sqrt{3},|\vec{a}|=|\vec{b}|=|\vec{c}|=1 \\ &|\vec{a}+\vec{b}|^{2}=(\sqrt{3})^{2} \\ \end{aligned}

\begin{aligned} &(\vec{a}+\vec{b})^{2}=(\sqrt{3})^{2} \\ &|\vec{a}|^{2}+|\vec{b}|^{2}+2(1)(1) \cos \theta=3 \\ \end{aligned}

\begin{aligned} &1+1+2 a \cdot b \cos \theta=3 \\ &2+2 \cos \theta=3 \\ &\cos \theta=1 \\ \end{aligned}

\begin{aligned} &\cos \theta=\frac{1}{2} \\ &\cos \theta=\cos 60^{\circ} \\ &\theta=\frac{\pi}{3} \end{aligned}

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