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Class 12 Three Dimensional Geometry · Short Answer2 Marksequations_of_lines

Class 12 Maths · Three Dimensional Geometry · Short Answer #34

Find vector and Cartesian equations through (1,2,−1) parallel to 5x−25=14−7y=35z. The latter line has direction (1/5,−1/7,1/35).

✅ Step-by-Step Solution

Final Answer: r=(1,2,-1)+t(7,-5,1), t∈ℝ; Cartesian: (x−(1))/(7)=(y−(2))/(-5)=(z−(-1))/(1).
  1. A line through A with nonzero direction d is r=A+td.
  2. Here A=(1,2,-1), d=(7,-5,1). Its components are x=7*t + 1, y=2 - 5*t, z=t - 1.
  3. r=(1,2,-1)+t(7,-5,1), t∈ℝ; Cartesian: (x−(1))/(7)=(y−(2))/(-5)=(z−(-1))/(1).

📋 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,-1), d=(7,-5,1). Its components are x=7*t + 1, y=2 - 5*t, z=t - 1.
  • [0.5 marks] r=(1,2,-1)+t(7,-5,1), t∈ℝ; Cartesian: (x−(1))/(7)=(y−(2))/(-5)=(z−(-1))/(1).

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