Class 12 Three Dimensional Geometry · Long Answer3 Marksshortest_distance
Class 12 Maths · Three Dimensional Geometry · Long Answer #86
Find the shortest distance between r=(1,-2,3)+t(-1,1,-2), t∈ℝ and r=(1,-1,1)+t(1,2,2), t∈ℝ.
✅ Step-by-Step Solution
Final Answer: 2*sqrt(5)/5
- For nonparallel lines use D=|(B−A)·(d×e)|/|d×e|.
- B−A=(0,1,-2), d×e=(6,0,-3).
- The numerator is 6 and the denominator is 3*sqrt(5).
- Therefore D=2*sqrt(5)/5.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For nonparallel lines use D=|(B−A)·(d×e)|/|d×e|.
- [1 mark] B−A=(0,1,-2), d×e=(6,0,-3).
- [1 mark] The numerator is 6 and the denominator is 3*sqrt(5).
- [0.5 marks] Therefore D=2*sqrt(5)/5.
Master Chapter 11: Three Dimensional Geometry
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Three Dimensional Geometry.
← Previous Question
Find vector and Cartesian equations of a line through (1,-1,1) whose…
Next Question →Show that r=(2,2,3)+t(1,3,1), t∈ℝ and r=(2,3,4)+t(1,4,2), t∈ℝ…
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.