Class 12 Three Dimensional Geometry · Long Answer3 Marksshortest_distance
Class 12 Maths · Three Dimensional Geometry · Long Answer #50
Find the shortest distance between r=(1,2,-4)+t(2,3,6), t∈ℝ and r=(3,3,-5)+t(4,6,12), t∈ℝ.
✅ Step-by-Step Solution
Final Answer: sqrt(293)/7
- The directions are proportional. Use D=|(B−A)×d|/|d|.
- B−A=(2,1,-1), (B−A)×d=(9,-14,4).
- The squared distance is 293/49.
- Therefore D=sqrt(293)/7.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The directions are proportional. Use D=|(B−A)×d|/|d|.
- [1 mark] B−A=(2,1,-1), (B−A)×d=(9,-14,4).
- [1 mark] The squared distance is 293/49.
- [0.5 marks] Therefore D=sqrt(293)/7.
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