NCERT Class 12 · Ch 11 Exercise 11.1 · Q2
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.1 Question 2
Find direction cosines of a line equally inclined to the positive coordinate axes.
💡 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: (1,1,1)/√3 or (−1,−1,−1)/√3.
- Equal inclinations give l=m=n.
- Use l²+m²+n²=1 to obtain 3l²=1, so l=±1/√3.
- The signs must all agree to give equal directed inclinations; reversing orientation gives the other triple.
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