Class 12 Three Dimensional Geometry · Long Answer3 Marksline_intersections
Class 12 Maths · Three Dimensional Geometry · Long Answer #87
Show that r=(2,2,3)+t(1,3,1), t∈ℝ and r=(2,3,4)+t(1,4,2), t∈ℝ intersect and find their intersection.
✅ Step-by-Step Solution
Final Answer: (1,-1,2)
- Set A+td=B+ue and equate the three coordinates.
- Use A=(2,2,3),d=(1,3,1),B=(2,3,4),e=(1,4,2).
- Solving gives t=-1, u=-1; both substitutions give (1,-1,2).
- All three coordinate equations agree, so the lines intersect at (1,-1,2).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Set A+td=B+ue and equate the three coordinates.
- [1 mark] Use A=(2,2,3),d=(1,3,1),B=(2,3,4),e=(1,4,2).
- [1 mark] Solving gives t=-1, u=-1; both substitutions give (1,-1,2).
- [0.5 marks] All three coordinate equations agree, so the lines intersect at (1,-1,2).
Master Chapter 11: Three Dimensional Geometry
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Three Dimensional Geometry.
← Previous Question
Find the shortest distance between r=(1,-2,3)+t(-1,1,-2), t∈ℝ and…
Next Question →Find the foot and distance from P=(1,6,3) to r=(0,1,2)+t(1,2,3)…
More Practice Questions in Three Dimensional Geometry
Related Questions in Three Dimensional Geometry
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the foot of the perpendicular from (2,−3,4) to the y-axis.
Class 12 Three Dimensional Geometry · Mcq Single Correct
A line makes angles α,β,γ with the positive coordinate axes. Find cos 2α+cos 2β+cos 2γ.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the distance of (α,β,γ) from the y-axis.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find direction cosines of (x−1)/2=(1−y)/3=(2z−1)/12.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the acute angle between two distinct body diagonals of a cube.
Class 12 Three Dimensional Geometry · Mcq Single Correct
A line makes angles θ₁,θ₂,θ₃,θ₄ with the four body diagonals of a cube. Find Σ cos²θᵢ.