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  • Need solution for RD sharma maths class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 11

Need solution for RD sharma maths class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 11

Answers (1)

\frac{\pi}{3}

Hint:

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

Given:

                \left |\vec{a} \right |=1 , \left |\vec{b} \right |=3 and \left |a-b \right |=\sqrt{7}. Find Angle between a and b.

Solution:

 \left |\vec{a} \right |=1 , \left |\vec{b} \right |=3 and \left |a-b \right |=\sqrt{7}                                                                           … (i)

\left |a-b \right |=\sqrt{7}

          Squaring on both side we get

\begin{aligned} &|a-b|^{2}=(\sqrt{7})^{2} \\ &|\vec{a}|^{2}+|\vec{b}|^{2}-2|\vec{a}| \cdot|\vec{b}| \cos \theta=(\sqrt{7})^{2} \end{aligned}

From (i)

\begin{aligned} &(1)^{2}+(3)^{2}-2(1)(3) \cos \theta=7 \\ &1+9-6 \cos \theta=7 \\ &10-7=6 \cos \theta \\ \end{aligned}

\begin{aligned} &\frac{3}{6}=\cos \theta \\ &\cos \theta=\frac{1}{2} \\ &\theta=\frac{\pi}{3} \end{aligned}

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