NCERT Class 12 · Ch 11 Exercise 11.2 · Q13
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.2 Question 13
Find the shortest distance between (x+1)/7=(y+1)/(−6)=(z+1) and (x−3)=(y−5)/(−2)=(z−7).
💡 Concept Hints
- Identify the base point and a nonzero direction before applying a vector formula.
- Use dot products for angles, proportional directions for parallelism, and a triple product for skew-line distance.
✅ Step-by-Step Solution
Final Answer: 2*sqrt(29)
- For nonparallel directions, D=|(B−A)·(d×e)|/|d×e|.
- Here B−A=(4,6,8), d×e=(-4,-6,-8).
- The numerator is 116 and the denominator is 2*sqrt(29).
- Therefore D=2*sqrt(29).
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