Class 12 Three Dimensional Geometry · Long Answer3 Marksline_intersections
Class 12 Maths · Three Dimensional Geometry · Long Answer #82
Show that r=(1,1,-1)+t(3,-1,0), t∈ℝ and r=(4,0,-1)+t(2,0,3), t∈ℝ intersect and find their intersection.
✅ Step-by-Step Solution
Final Answer: (4,0,-1)
- Set A+td=B+ue and equate the three coordinates.
- Use A=(1,1,-1),d=(3,-1,0),B=(4,0,-1),e=(2,0,3).
- Solving gives t=1, u=0; both substitutions give (4,0,-1).
- All three coordinate equations agree, so the lines intersect at (4,0,-1).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Set A+td=B+ue and equate the three coordinates.
- [1 mark] Use A=(1,1,-1),d=(3,-1,0),B=(4,0,-1),e=(2,0,3).
- [1 mark] Solving gives t=1, u=0; both substitutions give (4,0,-1).
- [0.5 marks] All three coordinate equations agree, so the lines intersect at (4,0,-1).
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