Class 12 Vector Algebra · Short Answer2 Marksscalar_projection
Class 12 Maths · Vector Algebra · Short Answer #48
Find λ if the scalar projection of (λ,1,4) onto (2,6,3) is 4.
✅ Step-by-Step Solution
Final Answer: λ = 5.
- Use scalar projection (a · b)/|b| = 4.
- Here a · b = 2λ + 6 + 12 = 2λ + 18 and |b| = 7. Thus (2λ + 18)/7 = 4, giving 2λ = 10.
- Therefore λ = 5.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use scalar projection (a · b)/|b| = 4.
- [1 mark] Here a · b = 2λ + 6 + 12 = 2λ + 18 and |b| = 7. Thus (2λ + 18)/7 = 4, giving 2λ = 10.
- [0.5 marks] Therefore λ = 5.
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