Question

If the vectors $\hat{i}-x\hat{j}-y\hat{k}$ and $\hat{i}+x\hat{j}+y\hat{k}$ are orthogonal to each other, then what is the locus of the point (x, y) ?

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

Answer 1

The correct option is C A circle

When two vectors are orthogonal, then $a.b=0$

$(\hat{i}-x\hat{j}-y\hat{k}).(\hat{i}+x\hat{j}+y\hat{k})=0\Rightarrow 1-x^2-y^2=0\Rightarrow x^2+y^2=1$

It is an equation of a circle.

Thus, the locus of the point $(x,y)$ is a circle.