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  • please solve RD sharma class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 2 maths textbook solution

please solve RD sharma class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 2 maths textbook solution

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best_answer

\pm \frac{3}{4}Hint:

               \vec{a}+\lambda\vec{b}is perpendicular to\vec{a}-\lambda\vec{b}

Given:

               \left | \vec{a} \right |=3,\left | \vec{b} \right |=4 and \vec{a}+\lambda\vec{b} is perpendicular to \vec{a}-\lambda\vec{b} , then \lambda =

Solution:

\vec{a}+\lambda\vec{b} is perpendicular to \vec{a}-\lambda\vec{b}

\begin{aligned} &(a+\lambda b)(a-\lambda b)=0 \\ &a^{2}-\lambda \times(a \cdot b)+\lambda \times(b \cdot a)-\lambda^{2} \times|b|^{2}=0 \\ \end{aligned}

\begin{aligned} &a^{2}-\lambda^{2} \times b^{2}=0 \\ &\lambda=\pm \frac{|a|}{|b|}=\pm \frac{3}{4}\end{aligned}

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