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  • Provide Solution for RD Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer Question 37

Provide Solution for RD Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer Question 37

Answers (1)

Answer:  \lambda = \frac{5}{2}

Given:  \overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}} \& \overrightarrow{\mathrm{b}}=\hat{\mathrm{\imath}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}   and  \vec{a} \& \vec{b}   are perpendicular

Hint: Use the formula of perpendicular vectors.

Solution: if vectors are perpendicular, then,

\begin{aligned} &\Rightarrow(2 \hat{\imath}+\lambda \hat{\jmath}+\hat{\mathrm{k}}) \cdot(\hat{\imath}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})=0 \\ & \end{aligned}

\Rightarrow 2-2 \lambda+3=0 \\

\Rightarrow-2 \lambda+5=0 \\

\Rightarrow-2 \lambda=-5 \\

\Rightarrow 2 \lambda=5 \\

\Rightarrow \lambda=\frac{5}{2}

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