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  • Explain solution RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 8 maths

Explain solution RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 8 maths

Answers (1)

Answer:

Option (b) an ellipse

Hint:

You must know the value of  \vec{a} \cdot \vec{b}=0 , when \vec{a} \text { and } \vec{b}are perpendicular

Given:

\hat{i}-2 x \hat{j}+3 y \hat{k} \text { and } \hat{i}+2 x \hat{j}-3 y \hat{k} are perpendicular, locus (x, y)=?

Solution:

a=\hat{i}-2 x \hat{j}+3 y \hat{k} \text { and } b=\hat{i}+2 x \hat{j}-3 y \hat{k}

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

\begin{aligned} &(\hat{i}-2 x \hat{j}+3 y \hat{k}) \cdot(\hat{i}+2 x \hat{j}-3 y \hat{k})=0 \\\\ &1-4 x^{2}-9 y^{2}=0 \\\\ &4 x^{2}+9 y^{2}=1 \end{aligned}

This is the equation of ellipse

Hence, option (b) is correct

Posted by

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