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  • Please Solve RD Sharma Class 12 Chapter 23 Scalar or Dot Product Exercise Very Short Answer Question 3 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 23 Scalar or Dot Product Exercise Very Short Answer Question 3 Maths Textbook Solution.

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ANSWER: \frac{4}{\sqrt{51}}

GIVEN:  \hat{4} \hat{i}-3 \hat{j}+3 \hat{k} \quad \& \quad 2 \hat{i}-\hat{j}-\hat{k}

HINTS: you must know the formula of cosθ

SOLUTION:We know that

\begin{aligned} &\cos \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|} \\ & \end{aligned}

\Rightarrow \cos \theta=\frac{(4 \hat{i}-3 \hat{j}+3 \hat{k}) \cdot(2 \hat{i}-\hat{j}-\hat{k})}{\sqrt{16+9+9} \sqrt{4+1+1}}

\begin{aligned} &\Rightarrow \cos \theta=\frac{8+3-3}{\sqrt{34} \sqrt{6}}=\cos \theta=\frac{8}{2 \sqrt{51}} \\ & \end{aligned}

\Rightarrow \cos \theta=\frac{4}{\sqrt{51}}

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