NCERT Class 12 · Ch 11 Exercise 11.2 · Q10
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.2 Question 10
Find p so that the directions of (1−x)/3=(7y−14)/(2p)=(z−3)/2 and (7−7x)/(3p)=(y−5)=(6−z)/5 are orthogonal.
💡 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: p=70/11.
- With common parameters, directions are d=(−3,2p/7,2) and e=(−3p/7,1,−5).
- Set d·e=0: 9p/7+2p/7−10=0.
- Thus 11p/7=10, giving p=70/11≠0, consistent with the printed denominators.
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