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  • Provide solution for RD Sharma maths class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 18

Provide solution for RD Sharma maths class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 18

Answers (1)

Answer:

Option (c) 0

Hint:

Use the identity \left(a^{2}-b^{2}\right)=(a-b)(a+b)

Given:

|\vec{a}|=|\vec{b}|,(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=?

Solution:

\begin{aligned} &(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=|\vec{a}|^{2}-|\vec{b}|^{2} \quad\left[\because(a+b)(a-b)=a^{2}-b^{2}\right] \\\\ &(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=0 &{[\because|\vec{a}|=|\vec{b}|]} \end{aligned}

Hence, option (c) is correct

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