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

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

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ANSWER:  3

GIVEN:  |\vec{b}|=1 \quad \&(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=8

HINTS:Use the identity of  \left(a^{2}-b^{2}\right)

SOLUTION:

\begin{aligned} &(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=8 \\ & \end{aligned}

\Rightarrow|\vec{a}|^{2}-|\vec{b}|^{2}=8\left[\because(a+b)(a-b)=a^{2}-b^{2}\right] \\

\Rightarrow|\vec{a}|^{2}-1=8 \quad\left[\because|\vec{b}|^{2}=1\right] \\

\Rightarrow|\vec{a}|^{2}=9 \\

\Rightarrow|\vec{a}|=3

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