Class 12 Vector Algebra · Short Answer2 Marksvector_identities
Class 12 Maths · Vector Algebra · Short Answer #53
If |v| = a, find |v × i|² + |v × j|² + |v × k|².
✅ Step-by-Step Solution
Final Answer: 2a².
- Write v = (x,y,z), with x² + y² + z² = a².
- The squared cross-product magnitudes are y² + z², x² + z² and x² + y². Their sum is 2(x² + y² + z²).
- Therefore the required value is 2a².
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write v = (x,y,z), with x² + y² + z² = a².
- [1 mark] The squared cross-product magnitudes are y² + z², x² + z² and x² + y². Their sum is 2(x² + y² + z²).
- [0.5 marks] Therefore the required value is 2a².
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