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  • Provide Solution for RD Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer Question 10

Provide Solution for RD Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer Question 10

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ANSWER: 4

GIVEN:  |\vec{a}|=|\vec{b}|, \theta=60^{\circ} \quad \& \quad \vec{a} \cdot \vec{b}=8

HINTS: use the formula of cosθ

SOLUTION:Let,

  $$ |\vec{a}|=|\vec{b}|=x

We know that

\cos \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}

\begin{aligned} &\Rightarrow \cos 60^{\circ}=\frac{8}{xx x}\qquad\left[\because \theta=60^{\circ}, \vec{a} \cdot \vec{b}=8, \overline{\mid a}|=| \vec{b} \mid=x\right] \\ & \end{aligned}

\Rightarrow \frac{1}{2}=\frac{8}{x^{2}} \qquad\left[\because \cos 60^{\circ}=\frac{1}{2}\right] \\

\Rightarrow x^{2}=16 \\

\Rightarrow x=4 \\

\therefore|\vec{a}|=\vec{|b|}=4

 

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