Class 12 Three Dimensional Geometry · Long Answer3 Marksprojection_and_reflection
Class 12 Maths · Three Dimensional Geometry · Long Answer #43
Find the foot and distance from P=(1,2,3) to r=(4,2,2)+t(2,3,6), t∈ℝ.
✅ Step-by-Step Solution
Final Answer: Foot H=(4,2,2); distance=sqrt(10).
- Write H=A+td and impose (P−H)·d=0.
- A=(4,2,2), d=(2,3,6), P−A=(-3,0,1); t=((P−A)·d)/(d·d)=0.
- H=A+td=(4,2,2). Check (P−H)·d=0.
- |P−H|=√(10)=sqrt(10). Foot H=(4,2,2); distance=sqrt(10).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write H=A+td and impose (P−H)·d=0.
- [1 mark] A=(4,2,2), d=(2,3,6), P−A=(-3,0,1); t=((P−A)·d)/(d·d)=0.
- [1 mark] H=A+td=(4,2,2). Check (P−H)·d=0.
- [0.5 marks] |P−H|=√(10)=sqrt(10). Foot H=(4,2,2); distance=sqrt(10).
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