NCERT Class 12 · Ch 11 Exercise 11.2 · Q4
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.2 Question 4
Find a line through (1,2,3) parallel to (3,2,−2).
💡 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: r=(1,2,3)+t(3,2,-2), t∈ℝ; Cartesian: (x−(1))/(3)=(y−(2))/(2)=(z−(3))/(-2).
- A line through base A in nonzero direction d has r=A+td.
- Here A=(1,2,3), d=(3,2,-2).
- Equating components gives r=(1,2,3)+t(3,2,-2), t∈ℝ. Eliminating t gives (x−(1))/(3)=(y−(2))/(2)=(z−(3))/(-2).
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