CBSE Class 12 Mathematics 2026 Main Paper 65/4/3 · Q355 Markspoint_line_distance
CBSE Class 12 Mathematics 2026 Main Paper 65/4/3 · Question 35 (Three Dimensional Geometry)
Find the distance from P=(1,2,3) to (x−6)/3=(y−7)/2=(z−7)/(−2). Find the perpendicular line through P and its foot.
✅ Step-by-Step Solution
Final Answer: Distance 7, foot (3,5,9), perpendicular r=(1,2,3)+t(2,3,6).
- Write the foot as H=(6+3s,7+2s,7−2s).
- Orthogonality of H−P with (3,2,−2) yields 17s+17=0, hence H=(3,5,9).
- The displacement is (2,3,6), with norm 7. It also gives the perpendicular line direction.
📋 CBSE Stepwise Marking Scheme
- [1 mark] Write the foot as H=(6+3s,7+2s,7−2s).
- [3 marks] Orthogonality of H−P with (3,2,−2) yields 17s+17=0, hence H=(3,5,9).
- [1 mark] The displacement is (2,3,6), with norm 7. It also gives the perpendicular line direction.
