Class 12 Three Dimensional Geometry · Long Answer3 Marksshortest_distance
Class 12 Maths · Three Dimensional Geometry · Long Answer #81
Find the shortest distance between r=(1,2,-1)+t(2,-3,4), t∈ℝ and r=(-2,3,0)+t(-1,2,3), t∈ℝ.
✅ Step-by-Step Solution
Final Answer: 7*sqrt(390)/65
- For nonparallel lines use D=|(B−A)·(d×e)|/|d×e|.
- B−A=(-3,1,1), d×e=(-17,-10,1).
- The numerator is 42 and the denominator is sqrt(390).
- Therefore D=7*sqrt(390)/65.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For nonparallel lines use D=|(B−A)·(d×e)|/|d×e|.
- [1 mark] B−A=(-3,1,1), d×e=(-17,-10,1).
- [1 mark] The numerator is 42 and the denominator is sqrt(390).
- [0.5 marks] Therefore D=7*sqrt(390)/65.
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