Class 12 Vector Algebra · Long Answer3 Marksdot_product_angle
Class 12 Maths · Vector Algebra · Long Answer #78
Unit vectors a,b have a−√2b also unit. Find their angle.
✅ Step-by-Step Solution
Final Answer: π/4
- Square |a−√2b|=1.
- Use |a|=|b|=1 to obtain 1+2−2√2(a·b)=1, hence a·b=1/√2.
- As a,b are unit, cos θ=1/√2.
- Thus θ=π/4.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Square |a−√2b|=1.
- [1 mark] Use |a|=|b|=1 to obtain 1+2−2√2(a·b)=1, hence a·b=1/√2.
- [1 mark] As a,b are unit, cos θ=1/√2.
- [0.5 marks] Thus θ=π/4.
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