JEE Main 2021 · 26 August · evening · Single correct · +4 / −1
The angle between vector (A⃗) and (A⃗-B⃗) is :
- (a) tan⁻¹((-B/2)/(A-B√3/2))
- (b) tan⁻¹(A/0.7B)
- (c) tan⁻¹(√3B/(2A-B))
- (d) tan⁻¹((B cos θ)/(A-B sin θ))
Answer and solution
Answer (c) tan⁻¹(√3B/(2A-B))
Solution
Physics sir · 3 steps
Read the angle between A and minus B off the figure first, then use the tan formula for a resultant.
- Angle between vectors. In the figure B⃗ starts at the head of A⃗, and the 120° is the inside angle of that triangle. Placed tail to tail, A⃗ and B⃗ make 180° - 120° = 60°, so A⃗ and -B⃗ make 120°.
- Treat as addition. Write A⃗-B⃗ = A⃗ + (-B⃗). This is the sum of two vectors of sizes A and B at angle α = 120°. The angle β it makes with A⃗ follows from the standard formula.
tan β = (B sin α)/(A + B cos α) = (B sin 120°)/(A + B cos 120°) = (√3/2B)/(A - B/2)
- So. Multiply the top and bottom by 2 to get β = tan⁻¹(√3B/(2A - B)), which is option (c).
The idea to keep. For the angle a resultant makes with A⃗, use tan β = (B sin α)/(A + B cos α). For A⃗-B⃗, first flip B⃗, which changes α to 180° - α.
Answer from the NTA final answer key. Solution by PrepWiser.