Class 12 Vector Algebra · Short Answer2 Marksvector_identities
Class 12 Maths · Vector Algebra · Short Answer #55
Given |a| = 10, |b| = 2 and |a × b| = 16, find all possible a · b.
✅ Step-by-Step Solution
Final Answer: a · b = ±12.
- Use (a · b)² = |a|²|b|² − |a × b|².
- Substitute to get (a · b)² = 100·4 − 256 = 144.
- Therefore a · b = ±12; no information selects the acute or obtuse angle.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use (a · b)² = |a|²|b|² − |a × b|².
- [1 mark] Substitute to get (a · b)² = 100·4 − 256 = 144.
- [0.5 marks] Therefore a · b = ±12; no information selects the acute or obtuse angle.
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