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

Question

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 (A) a circle (B) an ellipse (C) a parabola (D) a straight line

Tardigrade Admin · Accepted Answer

Since, vectors are orthogonal. ∴ ( i -2 x j -3 y k ) ⋅( i +3 x j +2 y k )=0 ⇒ 1-6 x2-6 y2=0 ⇒ x2+y2=(1/6) Hence, the locus of a point is a circle.

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

a circle

an ellipse

a parabola

a straight line

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

Q. If the vectors i−2xj−3yk and i+3xj+2yk are orthogonal to each other, then the locus of the point (x,y) is