NCERT Class 12 · Ch 11 Exercise 11.1 · Q5
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.1 Question 5
Find direction cosines of the sides of triangle A(3,5,−4),B(−1,1,2),C(−5,−5,−2). Use orientations AB,BC,CA.
💡 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: For those orientations: AB: (-2*sqrt(17)/17,-2*sqrt(17)/17,3*sqrt(17)/17); BC: (-2*sqrt(17)/17,-3*sqrt(17)/17,-2*sqrt(17)/17); CA: (2*sqrt(42)/21,5*sqrt(42)/42,-sqrt(42)/42). Reversed sides have opposite triples.
- Compute AB=(-4,-4,6), BC=(-4,-6,-4), CA=(8,10,-2).
- Their norms are 2*sqrt(17), 2*sqrt(17), 2*sqrt(42), respectively.
- Divide each direction by its norm: AB: (-2*sqrt(17)/17,-2*sqrt(17)/17,3*sqrt(17)/17); BC: (-2*sqrt(17)/17,-3*sqrt(17)/17,-2*sqrt(17)/17); CA: (2*sqrt(42)/21,5*sqrt(42)/42,-sqrt(42)/42).
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