Mathbee CBSE Mathbee · CBSE Class 12 Maths
CBSE Class 12 Mathematics 2026 Main Paper 65/4/2 · Q355 Marksline_intersection

CBSE Class 12 Mathematics 2026 Main Paper 65/4/2 · Question 35 (Three Dimensional Geometry)

Find the line through the intersection of r=(1,1,−1)+λ(3,−1,0) and r=(4,0,−1)+μ(2,0,3), parallel to (x−1)/(−2)=(7−y)/(−3)=z. Give vector and Cartesian equations.

✅ Step-by-Step Solution

Final Answer: r=(4,0,−1)+t(−2,3,1); (x−4)/(−2)=y/3=z+1.
  1. The y- and z-coordinates imply λ=1 and μ=0. The x-coordinates then agree at 4.
  2. Rewrite the given parallel line in terms of its common parameter to read direction (−2,3,1).
  3. Use that direction through (4,0,−1) in vector and Cartesian form.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] The y- and z-coordinates imply λ=1 and μ=0. The x-coordinates then agree at 4.
  • [3 marks] Rewrite the given parallel line in terms of its common parameter to read direction (−2,3,1).
  • [1 mark] Use that direction through (4,0,−1) in vector and Cartesian form.

Master Chapter 11: Three Dimensional Geometry

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Three Dimensional Geometry.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Evaluate \(\int x\,dx/[(x-1)(x^2+4)]\). OR Evaluate \(\int_0^1…
Next Question →
Box I contains 30 red caps, Box II contains 20 red and 10 green…

All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/4/2

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

Related Questions in Three Dimensional Geometry

Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the foot of the perpendicular from (2,−3,4) to the y-axis.
Class 12 Three Dimensional Geometry · Mcq Single Correct
A line makes angles α,β,γ with the positive coordinate axes. Find cos 2α+cos 2β+cos 2γ.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the distance of (α,β,γ) from the y-axis.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find direction cosines of (x−1)/2=(1−y)/3=(2z−1)/12.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the acute angle between two distinct body diagonals of a cube.
Class 12 Three Dimensional Geometry · Mcq Single Correct
A line makes angles θ₁,θ₂,θ₃,θ₄ with the four body diagonals of a cube. Find Σ cos²θᵢ.