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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A line is drawn from the point P 1,1 , 1 and perpendicular to a line whose direction ratios are 1,1 , 1 to intersect the plane x + 2 y + 3 z = 4 at the point Q . The locus of Q is

Options

  1. Ax 1 = y - 5 - 2 = z + 2 1
  2. Bx - 2 = y - 5 1 = z + 2 1
  3. Cx = y = z
  4. Dx 2 = y 3 = 2 5

Correct answer

A. x 1 = y - 5 - 2 = z + 2 1

Step-by-step solution

Let point Q is x 1 , y 1 , z 1 D.R’s of P Q are x 1 - 1 , y 1 - 1 , z 1 - 1 ⇒ 1 x 1 - 1 + 1 y 1 - 1 + 1 z 1 - 1 = 0 ⇒ x 1 + y 1 + z 1 = 3 Also x 1 + 2 y 1 + 3 z 1 = 4 x 1 + y 1 + z 1 = 3 ⇒ x 1 , y 1 , z 1 is a point on the two planes x + 2 y + 3 z = 4 x + y + z = 3 ∴ the line on the intersection of these two planes will be the required locus Now, the direction vector of the line is i ^ j ^ k ^ 1 1 1 1 2 3 = i ^ - 2 j ^ + k ^ Also, the point 0 , 5 , - 2 satisfy both the equation of plan

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