If the vectors $\hat{i}-2x\hat{j}+3y\hat{k}$ and $\hat{i}+2x\hat{j}-3y\hat{k}$ are perpendicular, then the locus of (x, y) is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → an ellipse
We are given two vectors,
$A=\hat{i}-2x\hat{j}+3y\hat{k}$
$B=\hat{i}+2x\hat{j}-3y\hat{k}$
if the vectors are perpendicular,
$A.B=0$
$A.B=(1)(1)+(-2x)(2x)+(3y)(-3y)$
$=1-4x^2-9y^2$
∴ it is an ellipse.