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COMEDK2014MathematicsThree Dimensional Geometry

From a point P(a, b, c) perpendicular P A, P B are drawn to y z and z x planes. Find the equation of the plane O A B , where O is the origin.

Options

  1. Ab c x+c a y+a b z=0
  2. Bb c x+c a y-a b z=0
  3. Cb c x-c a y+a b z=0
  4. D-b c x+c a y+a b z=0

Correct answer

B. b c x+c a y-a b z=0

Step-by-step solution

P(a, b, c) and P A and P B are perpendicular to Y Z and Z X planes. Hence, coordinate of A and B are (0, b, c) and (a, 0, c) respectively. Equation of plane passing through (0,0,0),(0, b, c) and aligned &(a, 0, c) is | array lll x & y & z 0 & b & c a & 0 & c array |=0 & x(b c-0)-y(0-a c)+z(0-a b)=0 & b c x+a c y-a b z=0 aligned

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