Class 12 Three Dimensional Geometry · Short Answer2 Marksequations_of_lines
Class 12 Maths · Three Dimensional Geometry · Short Answer #39
Find vector and Cartesian equations of the line through (1,2,3) with direction (3,2,-2).
✅ 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 A with nonzero direction d is r=A+td.
- Here A=(1,2,3), d=(3,2,-2). Its components are x=3*t + 1, y=2*t + 2, z=3 - 2*t.
- r=(1,2,3)+t(3,2,-2), t∈ℝ; Cartesian: (x−(1))/(3)=(y−(2))/(2)=(z−(3))/(-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=(3,2,-2). Its components are x=3*t + 1, y=2*t + 2, z=3 - 2*t.
- [0.5 marks] r=(1,2,3)+t(3,2,-2), t∈ℝ; Cartesian: (x−(1))/(3)=(y−(2))/(2)=(z−(3))/(-2).
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