Class 12 Vector Algebra · Short Answer2 Markscross_product_angle
Class 12 Maths · Vector Algebra · Short Answer #59
If |a| = 3, |b| = 2/3 and a × b is a unit vector, find all possible angles between a,b.
✅ Step-by-Step Solution
Final Answer: θ = π/6 or 5π/6.
- The unit cross product gives |a||b|sin θ = 1, with θ ∈ [0,π].
- Thus 2sin θ = 1 and sin θ = 1/2.
- Therefore θ = π/6 or 5π/6. Both satisfy the data.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The unit cross product gives |a||b|sin θ = 1, with θ ∈ [0,π].
- [1 mark] Thus 2sin θ = 1 and sin θ = 1/2.
- [0.5 marks] Therefore θ = π/6 or 5π/6. Both satisfy the data.
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