Class 12 Three Dimensional Geometry · Short Answer2 Marksequations_of_lines
Class 12 Maths · Three Dimensional Geometry · Short Answer #40
Find vector and Cartesian equations of the line through (2,-1,4) with direction (1,2,-1).
✅ 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 A with nonzero direction d is r=A+td.
- Here A=(2,-1,4), d=(1,2,-1). Its components are x=t + 2, y=2*t - 1, z=4 - t.
- r=(2,-1,4)+t(1,2,-1), t∈ℝ; Cartesian: (x−(2))/(1)=(y−(-1))/(2)=(z−(4))/(-1).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] A line through A with nonzero direction d is r=A+td.
- [1 mark] Here A=(2,-1,4), d=(1,2,-1). Its components are x=t + 2, y=2*t - 1, z=4 - t.
- [0.5 marks] r=(2,-1,4)+t(1,2,-1), t∈ℝ; Cartesian: (x−(2))/(1)=(y−(-1))/(2)=(z−(4))/(-1).
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