Class 12 Three Dimensional Geometry · Very Long Answer5 Marksline_intersections
Class 12 Maths · Three Dimensional Geometry · Very Long Answer #51
Find b so that r=(1,b,3)+t(2,3,4) and r=(4,1,0)+u(5,2,1) intersect. Find their intersection.
✅ Step-by-Step Solution
Final Answer: b=2; intersection (−1,−1,−1).
- Equate coordinates: 1+2t=4+5u, b+3t=1+2u, 3+4t=u.
- The first and third equations give 2t−5u=3 and u=3+4t.
- Substitute: −18t=18, so t=−1 and u=−1.
- The y equation becomes b−3=−1, giving b=2.
- Both lines then pass through (−1,−1,−1).
📋 CBSE Stepwise Marking Scheme
- [1 mark] Equate coordinates: 1+2t=4+5u, b+3t=1+2u, 3+4t=u.
- [1 mark] The first and third equations give 2t−5u=3 and u=3+4t.
- [1 mark] Substitute: −18t=18, so t=−1 and u=−1.
- [1 mark] The y equation becomes b−3=−1, giving b=2.
- [1 mark] Both lines then pass through (−1,−1,−1).
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