Class 12 Three Dimensional Geometry · Very Long Answer5 Marksshortest_distance
Class 12 Maths · Three Dimensional Geometry · Very Long Answer #90
Find the shortest distance between r=(1,2,3)+t(2,3,4), t∈ℝ and r=(2,4,5)+t(2,6,3), t∈ℝ.
✅ Step-by-Step Solution
Final Answer: sqrt(265)/265
- For nonparallel lines use D=|(B−A)·(d×e)|/|d×e|.
- B−A=(1,2,2), d×e=(-15,2,6).
- The numerator is 1 and the denominator is sqrt(265).
- Distance is nonnegative; take the nonnegative square root after simplifying.
- Therefore D=sqrt(265)/265.
📋 CBSE Stepwise Marking Scheme
- [1 mark] For nonparallel lines use D=|(B−A)·(d×e)|/|d×e|.
- [1 mark] B−A=(1,2,2), d×e=(-15,2,6).
- [1 mark] The numerator is 1 and the denominator is sqrt(265).
- [1 mark] Distance is nonnegative; take the nonnegative square root after simplifying.
- [1 mark] Therefore D=sqrt(265)/265.
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