Class 12 Three Dimensional Geometry · Very Long Answer5 Marksprojection_and_reflection
Class 12 Maths · Three Dimensional Geometry · Very Long Answer #57
If (a,b,c) is the reflection of (1,2,−3) in (x+1)/2=(y−3)/(−2)=z/(−1), find a+b+c.
✅ Step-by-Step Solution
Final Answer: 2.
- Take A=(−1,3,0), d=(2,−2,−1), P=(1,2,−3).
- The foot H=A+td satisfies t=((P−A)·d)/(d·d)=(4+2+3)/9=1.
- Hence H=(1,1,−1).
- The reflection is 2H−P=(1,0,1).
- Thus a+b+c=1+0+1=2.
📋 CBSE Stepwise Marking Scheme
- [1 mark] Take A=(−1,3,0), d=(2,−2,−1), P=(1,2,−3).
- [1 mark] The foot H=A+td satisfies t=((P−A)·d)/(d·d)=(4+2+3)/9=1.
- [1 mark] Hence H=(1,1,−1).
- [1 mark] The reflection is 2H−P=(1,0,1).
- [1 mark] Thus a+b+c=1+0+1=2.
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