AP EAMCET · Maths · Vector Algebra
If the vectors \(\mathbf{i}-2 x \mathbf{j}-3 y \mathbf{k}\) and \(\mathbf{i}+3 x \mathbf{j}+2 y \mathbf{k}\) 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
Answer & Solution
Correct Answer
(A) a circle
Step-by-step Solution
Detailed explanation
Since, vectors are orthogonal. \(\begin{aligned} & \therefore \quad(\mathbf{i}-2 x \mathbf{j}-3 y \mathbf{k}) \cdot(\mathbf{i}+3 x \mathbf{j}+2 y \mathbf{k})=0 \\ & \Rightarrow \quad 1-6 x^2-6 y^2=0 \Rightarrow x^2+y^2=\frac{1}{6} \end{aligned}\) Hence, the locus of a point is a…
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