Class 12 Vector Algebra · Long Answer3 Marksdot_product_angle
Class 12 Maths · Vector Algebra · Long Answer #70
If a+b+c=0 and |a|=3, |b|=5, |c|=7, prove the angle between a,b is 60°.
✅ Step-by-Step Solution
Final Answer: 60°
- Since a+b=−c, square the norms to get |a|²+|b|²+2a·b=|c|².
- Thus 9+25+2a·b=49, so a·b=15/2.
- Then cos θ=(15/2)/(3·5)=1/2.
- For θ∈[0,π], θ=π/3=60°.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Since a+b=−c, square the norms to get |a|²+|b|²+2a·b=|c|².
- [1 mark] Thus 9+25+2a·b=49, so a·b=15/2.
- [1 mark] Then cos θ=(15/2)/(3·5)=1/2.
- [0.5 marks] For θ∈[0,π], θ=π/3=60°.
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