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NDA 2 2024 Maths, question 70

Topic: Analytical geometry

Passage · Q69 to Q70

Let L:x+y+z+4=0=2x−y−z+8L:x+y+z+4=0=2x-y-z+8 be a line and P:x+2y+3z+1=0P:x+2y+3z+1=0 be a plane.

Q70

What is the point of intersection of LL and PP?

  1. (a) (4,3,−3)(4,3,-3)
  2. (b) (4,−3,3)(4,-3,3)
  3. (c) (−4,−3,−3)(-4,-3,-3)
  4. (d) (−4,−3,3)(-4,-3,3)Correct answer

Solution.

Answer: (d) (−4,−3,3)(-4,-3,3)

  1. Add the two line-defining equations to get 3x+12=0, so x=−4.
  2. Then y+z=0.
  3. The third plane gives −4+2y+3z+1=0; with y=−z, obtain z=3 and y=−3.
  4. The point (−4,−3,3) satisfies all three equations.