Question

The vectors $\hat{i}-2x\hat{j}-3y\hat{k}$ and $\hat{i}+3x\hat{j}+2y\hat{k}$ are orthogonal to each other. Then the locus of the point $(x,y)$ is

• A. Hyperbola
• B. Ellipse
• C. Parabola
• D. Circle

Answer 1

The correct option is D Circle

Two vectors are orthogonal if their dot product is $0$.

So here,

$\widehat{(i-}2x\hat{j}-3y\widehat{k).(}\hat{i}+3x\hat{j}+2y\widehat{k)}=0$

$\Rightarrow 1-6x^2-6y^2=0$

$\Rightarrow x^2+y^2=\frac{1}{6}$

So the locus is a circle.

Hence, D is correct.