Question

If 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. A circle
• B. An ellipse
• C. A parabola
• D. A straight line

Answer 1

The correct option is A A circle

Points are orthogonal, so dot product of them is zero

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

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

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

which is a circle.