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  • Need solution for RD Sharma maths class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 15

Need solution for RD Sharma maths class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 15

Answers (1)

Answer:

Option (c) 14

Hint:

If \vec{a} \text { and } \vec{b} are perpendicular, then \vec{a} \cdot \vec{b}=0

Given:

3 \hat{i}+\lambda \hat{j}+\hat{k} \text { and } 2 \hat{i}-\hat{j}+8 \hat{k}  are perpendicular.

Solution:

Let \vec{a}=3 \hat{i}+\lambda \hat{j}+\hat{k} \text { and } \vec{b}=2 \hat{i}-\hat{j}+8 \hat{k}

If \vec{a} \text { and } \vec{b} are perpendicular, then \vec{a} \cdot \vec{b}=0

\begin{aligned} &(3 \hat{i}+\lambda \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+8 \hat{k})=0 \\\\ &6-\lambda+8=0 \\\\ &-\lambda+14=0 \\\\ &-\lambda=-14 \\\\ &\lambda=14 \end{aligned}

Hence option (c) is correct

 

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