NCERT Class 12 · Ch 11 Exercise 11.1 · Q1
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.1 Question 1
A directed line makes angles 90°,135°,45° with the positive x,y,z axes. Find its direction cosines.
💡 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: (0,−1/√2,1/√2).
- Direction cosines are cos α,cos β,cos γ.
- cos 90°=0, cos 135°=−1/√2 and cos 45°=1/√2. Their squared sum is 0+1/2+1/2=1.
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