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  • Provide solution for RD sharma maths class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 7

Provide solution for RD sharma maths class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 7

Answers (1)

\frac{2\pi}{3}

Hint:

Angle between \vec{a} andn \vec{b}

Given:

If \vec{a},\vec{b},\vec{c} are unit vector such that \vec{a}+\vec{b}-\vec{c}=0, then angle betweenaandbis

Solution:

               \left |\vec{a} \right |=\left |\vec{b} \right |=\left |\vec{c} \right |=1

We have,

\vec{a}+\vec{b}-\vec{c}=0             

\vec{a}+\vec{b}=\vec{c}

on squaring both sides,

\begin{aligned} &(\vec{a}+\vec{b})^{2}=(\vec{c})^{2} \\ &|\vec{a}|^{2}+|\vec{b}|^{2}+2 \cdot a \cdot b \cos \theta=(\vec{c})^{2} \\ \end{aligned}

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

\begin{aligned} &\cos \theta(1)(1)=\frac{-1}{2} \\ &\cos \theta=\frac{-1}{2} \\ &\theta=\frac{2 \pi}{3} \end{aligned}

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