If the vectors `-hat(i)-2xhat(j)-3y hat(k) and hat(i)-3x hat(j)-2y hat(k)` are orthogonal to each other, then what is the locus of the point (x, y) ?

Options

A. a straight line
B. an ellipse
C. A parabola
D. a circle

Answer

D

Explanation

Given vectors `-hat(i)-2xhat(j)-3 y hat(k) and hat(i)-3xhat(j)-2yhat(k)` are orthogonal to each other.
`:. (-hat(i)-2xhat(j)-3y hat(k)).(hat(i)-3xhat(j)-2y hat(k))=0`
`rArr (-1)(1)+(-2x)(-3x)+(-3y)(-2y)=0`
`rArr -1+6x^(2)+6y^(2)=0`
`rArr 6x^(2)+6y^(2)=1`
`rArr x^(2)+y^(2)=((1)/(sqrt(6)))^(2)`
Hence. locus of (x, y) is a circle.