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  4. If the vectors i -2 x j -3 y k and i +3 x j +2 y k are orthogonal to each other, then the locus of the point (x, y) is

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Q. If the vectors $i -2 x j -3 y k$ and $i +3 x j +2 y k$ are orthogonal to each other, then the locus of the point $(x, y)$ is

EAMCETEAMCET 2011

Solution:

Since, vectors are orthogonal.
$\therefore ( i -2 x j -3 y k ) \cdot( i +3 x j +2 y k )=0$
$\Rightarrow 1-6 x^{2}-6 y^{2}=0$
$ \Rightarrow x^{2}+y^{2}=\frac{1}{6}$
Hence, the locus of a point is a circle.