NCERT Class 12 · Ch 11 Exercise 11.1 · Q3
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.1 Question 3
Find direction cosines for a line with direction ratios (−18,12,−4).
💡 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: (−9,6,−2)/11, or its negative for the reversed orientation.
- The direction norm is √(18²+12²+4²)=√484=22.
- Divide (−18,12,−4) by 22 to get (−9,6,−2)/11.
- The squared components sum to (81+36+4)/121=1.
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