Class 12 Vector Algebra · Long Answer3 Marksorthogonality
Class 12 Maths · Vector Algebra · Long Answer #113
Let p=(5,λ,−3), q=(1,3,−5). Find λ so p+q and p−q are perpendicular.
✅ Step-by-Step Solution
Final Answer: λ=±1
- Use (p+q)·(p−q)=|p|²−|q|².
- Perpendicularity requires 25+λ²+9=1+9+25.
- Thus λ²+34=35, giving λ²=1.
- Therefore λ=±1; both give nonzero perpendicular sum and difference vectors.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use (p+q)·(p−q)=|p|²−|q|².
- [1 mark] Perpendicularity requires 25+λ²+9=1+9+25.
- [1 mark] Thus λ²+34=35, giving λ²=1.
- [0.5 marks] Therefore λ=±1; both give nonzero perpendicular sum and difference vectors.
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