NCERT Class 12 · Ch 11 Exercise 11.2 · Q5
NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Exercise 11.2 Question 5
Find vector and Cartesian equations through (2,−1,4) with direction (1,2,−1).
💡 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=(2,-1,4)+t(1,2,-1), t∈ℝ; Cartesian: (x−(2))/(1)=(y−(-1))/(2)=(z−(4))/(-1).
- A line through base A in nonzero direction d has r=A+td.
- Here A=(2,-1,4), d=(1,2,-1).
- Equating components gives r=(2,-1,4)+t(1,2,-1), t∈ℝ. Eliminating t gives (x−(2))/(1)=(y−(-1))/(2)=(z−(4))/(-1).
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