Class 12 Vector Algebra · Long Answer3 Marksvector_identities
Class 12 Maths · Vector Algebra · Long Answer #63
If |a|=3, |b|=5, |c|=4 and a+b+c=0, find a·b+b·c+c·a.
✅ Step-by-Step Solution
Final Answer: −25
- Square a+b+c=0 using the dot product.
- Obtain |a|²+|b|²+|c|²+2(a·b+b·c+c·a)=0.
- Substitute 9+25+16+2S=0, giving 2S=−50.
- Therefore S=−25.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Square a+b+c=0 using the dot product.
- [1 mark] Obtain |a|²+|b|²+|c|²+2(a·b+b·c+c·a)=0.
- [1 mark] Substitute 9+25+16+2S=0, giving 2S=−50.
- [0.5 marks] Therefore S=−25.
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