Class 12 Vector Algebra · Short Answer2 Marksorthogonality
Class 12 Maths · Vector Algebra · Short Answer #54
Vectors a = (3,x,0) and b = (2,1,y) are perpendicular and have equal magnitudes. Find y.
✅ Step-by-Step Solution
Final Answer: y = ±2√10.
- Perpendicularity gives a · b = 6 + x = 0, so x = −6.
- Equal squared norms give 9 + x² = 5 + y². Substitute x = −6 to get 45 = 5 + y², hence y² = 40.
- Therefore y = ±2√10.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Perpendicularity gives a · b = 6 + x = 0, so x = −6.
- [1 mark] Equal squared norms give 9 + x² = 5 + y². Substitute x = −6 to get 45 = 5 + y², hence y² = 40.
- [0.5 marks] Therefore y = ±2√10.
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