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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

The vectors i-2 x j -3 y k and i +3 x j +2 y k are orthogonal to...

The vectors i−2xj^−3yk^i-2 x \hat{j}-3 y \hat{k} and i^+3xj^+2yk^\hat{i}+3 x \hat{j}+2 y \hat{k} are orthogonal to each other. Then the locus of the point (x,y)(x, y) is

Options

  1. Ahyperbola
  2. Bellipse
  3. Cparabola
  4. Dcircle

Correct answer

D. circle

Step-by-step solution

Two vectors are orthogonal, if its dot product or scalar product =0=0(i^−2xj^−3yk^)⋅(i^+3xj^+2yk^)=01−6x2−6y2=0 or, x2+y2=16\begin{aligned} & (\hat{i}-2 x \hat{j}-3 y \hat{k}) \cdot(\hat{i}+3 x \hat{j}+2 y \hat{k})=0 \\ & 1-6 x^2-6 y^2=0 \quad \text{ or, } x^2+y^2=\frac{1}{6} \end{aligned}$$ This is a circle.
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