Class 12 Three Dimensional Geometry · Very Long Answer5 Marksshortest_distance
Class 12 Maths · Three Dimensional Geometry · Very Long Answer #56
Find the shortest distance between r=(3,8,3)+t(3,-1,1), t∈ℝ and r=(-3,-7,6)+t(-3,2,4), t∈ℝ.
✅ Step-by-Step Solution
Final Answer: 3*sqrt(30)
- For nonparallel lines use D=|(B−A)·(d×e)|/|d×e|.
- B−A=(-6,-15,3), d×e=(-6,-15,3).
- The numerator is 270 and the denominator is 3*sqrt(30).
- Distance is nonnegative; take the nonnegative square root after simplifying.
- Therefore D=3*sqrt(30).
📋 CBSE Stepwise Marking Scheme
- [1 mark] For nonparallel lines use D=|(B−A)·(d×e)|/|d×e|.
- [1 mark] B−A=(-6,-15,3), d×e=(-6,-15,3).
- [1 mark] The numerator is 270 and the denominator is 3*sqrt(30).
- [1 mark] Distance is nonnegative; take the nonnegative square root after simplifying.
- [1 mark] Therefore D=3*sqrt(30).
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