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  • Need solution for RD Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Excercise Very Short Answer Question 6

Need solution for RD Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Excercise Very Short Answer Question 6

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ANSWER:  0

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

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

SOLUTION:

\begin{aligned} &|\vec{a}|=|\vec{b}| \& \text { ? } \\ & \end{aligned}

(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=|\vec{a}|^{2}-|\vec{b}|^{2} \qquad \qquad \qquad\left[\because(\mathrm{a}+\mathrm{b})(\mathrm{a}-\mathrm{b})=\mathrm{a}^{2}-b^{2}\right] \\

(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=|\vec{b}|^{2}-|\vec{b}|^{2} \qquad \qquad\qquad[\because|\vec{a}|=|\vec{b}|] \\

                               =0

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