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

Options

A. hyperbola
B. ellipse
C. parabola
D. circle

Answer

D

Explanation

`(hat(i)-2xhat(j)-3yhat(k)).(hat(i)+3x hat(j)+2 y hat(k))=0`
`1-6x^(2)-6y^(2)=0`
`-6x^(2)-6y^(2)=-1`
`x^(2)+y^(2)=(1)/(6)`
`x^(2)+y^(2)=(sqrt((1)/(6)))^(2)`
Hence, locus of the point i.e. a circle.