CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Q232 Markspoint_projection
CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Question 23 (Three Dimensional Geometry)
Find the foot from the origin to x=(y+1)/(−1)=(z−3)/(−2).
✅ Step-by-Step Solution
Final Answer: (5/6,−11/6,4/3).
- Parametrize the foot as H=(t,−1−t,3−2t) with line direction (1,−1,−2).
- The perpendicular condition H·(1,−1,−2)=0 gives 6t−5=0.
- Substitute t=5/6 to obtain (5/6,−11/6,4/3).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Parametrize the foot as H=(t,−1−t,3−2t) with line direction (1,−1,−2).
- [1 mark] The perpendicular condition H·(1,−1,−2)=0 gives 6t−5=0.
- [0.5 marks] Substitute t=5/6 to obtain (5/6,−11/6,4/3).
Master Chapter 11: Three Dimensional Geometry
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Three Dimensional Geometry.
← Previous Question
For AB=(0,1,1) and AC=(3,−1,4), prove AD=(AB+AC)/2 where D is the…
Next Question →Is f: ℝ∖{3}→ℝ, f(x)=(x−2)/(x−3), onto? OR Is f: ℤ×ℤ→ℤ×ℤ…
All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/2/2
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.