Class 12 Three Dimensional Geometry · Short Answer2 Marksequations_of_lines
Class 12 Maths · Three Dimensional Geometry · Short Answer #78
Find vector and Cartesian equations of the line through (1,2,3) with direction (-4,0,1).
✅ Step-by-Step Solution
Final Answer: r=(1,2,3)+t(-4,0,1), t∈ℝ; Cartesian: (x−(1))/(-4)=(z−(3))/(1); y=2.
- A line through A with nonzero direction d is r=A+td.
- Here A=(1,2,3), d=(-4,0,1). Its components are x=1 - 4*t, y=2, z=t + 3.
- r=(1,2,3)+t(-4,0,1), t∈ℝ; Cartesian: (x−(1))/(-4)=(z−(3))/(1); y=2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] A line through A with nonzero direction d is r=A+td.
- [1 mark] Here A=(1,2,3), d=(-4,0,1). Its components are x=1 - 4*t, y=2, z=t + 3.
- [0.5 marks] r=(1,2,3)+t(-4,0,1), t∈ℝ; Cartesian: (x−(1))/(-4)=(z−(3))/(1); y=2.
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