Class 12 Vector Algebra · Long Answer3 Marksvector_identities
Class 12 Maths · Vector Algebra · Long Answer #67
Given |a|=1, |b|=2, |c|=3, the scalar projections of b and c onto a are equal, and b⊥c, find |3a−2b+2c|.
✅ Step-by-Step Solution
Final Answer: √61
- Equal scalar projections give a·b=a·c, since |a|=1. Also b·c=0.
- Expand the squared norm: 9|a|²+4|b|²+4|c|²−12a·b+12a·c−8b·c.
- The mixed terms cancel or vanish, leaving 9+16+36=61.
- Therefore |3a−2b+2c|=√61.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Equal scalar projections give a·b=a·c, since |a|=1. Also b·c=0.
- [1 mark] Expand the squared norm: 9|a|²+4|b|²+4|c|²−12a·b+12a·c−8b·c.
- [1 mark] The mixed terms cancel or vanish, leaving 9+16+36=61.
- [0.5 marks] Therefore |3a−2b+2c|=√61.
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