Class 12 Three Dimensional Geometry · Long Answer3 Marksline_intersections
Class 12 Maths · Three Dimensional Geometry · Long Answer #84
Show that r=(0,-1,-1)+t(4,6,2), t∈ℝ and r=(3,9,4)+t(-7,-5,0), t∈ℝ intersect and find their intersection.
✅ Step-by-Step Solution
Final Answer: (10,14,4)
- Set A+td=B+ue and equate the three coordinates.
- Use A=(0,-1,-1),d=(4,6,2),B=(3,9,4),e=(-7,-5,0).
- Solving gives t=5/2, u=-1; both substitutions give (10,14,4).
- All three coordinate equations agree, so the lines intersect at (10,14,4).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Set A+td=B+ue and equate the three coordinates.
- [1 mark] Use A=(0,-1,-1),d=(4,6,2),B=(3,9,4),e=(-7,-5,0).
- [1 mark] Solving gives t=5/2, u=-1; both substitutions give (10,14,4).
- [0.5 marks] All three coordinate equations agree, so the lines intersect at (10,14,4).
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