NCERT Class 12 · Ch 11 Exercise 11.2 · Q11
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.2 Question 11
Show that (x−5)/7=(y+2)/(−5)=z and x=y/2=z/3 have orthogonal directions.
💡 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: The line angle is π/2; the lines are skew.
- The directions are (7,−5,1) and (1,2,3). Their dot product is 7−10+3=0.
- Thus their direction angle is π/2. This alone does not establish intersection.
- If (5,−2,0)+t(7,−5,1)=s(1,2,3), z gives t=3s. Then x gives s=−1/4, whereas y gives s=−2/17, a contradiction; they are skew.
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