Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Three Dimensional Geometry · Very Long Answer5 Marksangles_between_lines

Class 12 Maths · Three Dimensional Geometry · Very Long Answer #91

Find the acute angles between (i) (x−2)/2=(y−1)/5=(z+3)/(−3) and (x+2)/(−1)=(y−4)/8=(z−5)/4; (ii) x/2=y/2=z and (x−5)/4=(y−2)= (z−3)/8.

✅ Step-by-Step Solution

Final Answer: (i) cos⁻¹(26/(9√38)); (ii) cos⁻¹(2/3).
  1. Use cos θ=|d·e|/(|d||e|) for the acute line angle.
  2. In (i), d=(2,5,−3),e=(−1,8,4), with dot product 26.
  3. Their norms are √38 and 9, giving cos θ₁=26/(9√38).
  4. In (ii), d=(2,2,1),e=(4,1,8), with dot product 18 and norms 3 and 9.
  5. Thus θ₁=cos⁻¹(26/(9√38)), θ₂=cos⁻¹(2/3).

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Use cos θ=|d·e|/(|d||e|) for the acute line angle.
  • [1 mark] In (i), d=(2,5,−3),e=(−1,8,4), with dot product 26.
  • [1 mark] Their norms are √38 and 9, giving cos θ₁=26/(9√38).
  • [1 mark] In (ii), d=(2,2,1),e=(4,1,8), with dot product 18 and norms 3 and 9.
  • [1 mark] Thus θ₁=cos⁻¹(26/(9√38)), θ₂=cos⁻¹(2/3).

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 Interactive Workspace →
← Previous Question
Find the shortest distance between r=(1,2,3)+t(2,3,4), t∈ℝ and…
Next Question →
Find equations of diagonals and their intersection for parallelogram…

More Practice Questions in Three Dimensional Geometry

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

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.