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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Vector Algebra

NDA 2012 · Mathematics · Vector Algebra

If the vectors i -x j -y k and i +x j -y k are orthogonal to each...

If the vectors i^−xj^−yk^\hat{i}-x \hat{j}-y \hat{k} and i^+xj^−yk^\hat{i}+x \hat{j}-y \hat{k} are orthogonal to each other, then what is the locus of the point (x,y)(x, y) ?

Options

  1. Aa parabola
  2. Ban ellipse
  3. Ca circle
  4. Da straight line

Correct answer

B. an ellipse

Step-by-step solution

1(1)+(−x)(x)+(−y)(y)=01−x2−y2=0x2+y2=1.\begin{gathered}1(1)+(-x)(x)+(-y)(y)=0 \\ 1-x^2-y^2=0 \\ x^2+y^2=1.\end{gathered}
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