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Class 12 Three Dimensional Geometry · Long Answer3 Marksline_intersections

Class 12 Maths · Three Dimensional Geometry · Long Answer #46

Show that r=(-1,-3,-5)+t(3,5,7), t∈ℝ and r=(2,4,6)+t(1,3,5), t∈ℝ intersect and find their intersection.

✅ Step-by-Step Solution

Final Answer: (1/2,-1/2,-3/2)
  1. Set A+td=B+ue and equate the three coordinates.
  2. Use A=(-1,-3,-5),d=(3,5,7),B=(2,4,6),e=(1,3,5).
  3. Solving gives t=1/2, u=-3/2; both substitutions give (1/2,-1/2,-3/2).
  4. All three coordinate equations agree, so the lines intersect at (1/2,-1/2,-3/2).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Set A+td=B+ue and equate the three coordinates.
  • [1 mark] Use A=(-1,-3,-5),d=(3,5,7),B=(2,4,6),e=(1,3,5).
  • [1 mark] Solving gives t=1/2, u=-3/2; both substitutions give (1/2,-1/2,-3/2).
  • [0.5 marks] All three coordinate equations agree, so the lines intersect at (1/2,-1/2,-3/2).

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