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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

an ellipse

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a parabola

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a straight line

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A a circle
If given vectors are orthogonal then their dot product will be zero

$\Rightarrow 1 (1) - 2 x (3 x) - 3 y (2 y) = 0$
$\Rightarrow 6 x^{2} + 6 y^{2} = 1$

$\Rightarrow x^{2} + y^{2} = \frac{1}{6}$

Clearly it represents a circle

Suggest Corrections

Similar questions

\hat{i} - 2 x \hat{j} + 3 y \hat{k} and \hat{i} + 2 x \hat{j} - 3 y \hat{k}

^i - 2 x^j - 3 y^k a n d^i + 3 x^j + 2 y^k

^i - x^j - y^k

^i + x^j + y^k

(^i - 2 x^j - 3 y^k)

(^i + 3 x^j + 2 y^k)

(x, y)

^i - 2 x^j - 3 y^k

^i + 3 x^j + 2 y^k

(x, y)

Join BYJU'S Learning Program