Class 12 Three Dimensional Geometry · Short Answer2 Marksorthogonal_directions
Class 12 Maths · Three Dimensional Geometry · Short Answer #35
Show that the directions of r=(2,1,-3)+t(2,7,-3), t∈ℝ and r=(-2,8,5)+t(-1,2,4), t∈ℝ are orthogonal.
✅ Step-by-Step Solution
Final Answer: The directions are orthogonal; the lines are skew.
- Use d·e=0 to test direction orthogonality.
- d=(2,7,-3),e=(-1,2,4); d·e=0. The simultaneous coordinate equations have no common intersection.
- The nonzero directions are orthogonal. The lines do not meet, so they are skew rather than intersecting perpendicular lines.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use d·e=0 to test direction orthogonality.
- [1 mark] d=(2,7,-3),e=(-1,2,4); d·e=0. The simultaneous coordinate equations have no common intersection.
- [0.5 marks] The nonzero directions are orthogonal. The lines do not meet, so they are skew rather than intersecting perpendicular lines.
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