JEE Main 2024 · 5 April · morning · Single correct · +4 / −1
The angle between vector Q⃗ and the resultant of (2Q⃗+2P⃗) and (2Q⃗-2P⃗) is :
- (a) tan⁻¹(P/Q)
- (b) 0°
- (c) tan⁻¹(2Q⃗-2P⃗)/(2Q⃗+2P⃗)
- (d) tan⁻¹(2Q/P)
Answer and solution
Answer (b) 0°
Solution
Physics sir · 3 steps
Add the two vectors first: the P⃗ parts cancel, and whatever is left points exactly along Q⃗.
- Add the vectors. The resultant is the vector sum of the two given vectors. Add them term by term.
R⃗ = (2Q⃗ + 2P⃗) + (2Q⃗ - 2P⃗) = 4Q⃗
- Read the direction. +2P⃗ and -2P⃗ cancel exactly, so R⃗ = 4Q⃗. Multiplying a vector by a positive number changes only its length, not its direction.
- So. R⃗ points along Q⃗, so the angle between them is 0°, option (b).
The idea to keep. Before you reach for tan⁻¹ formulas, add the vectors algebraically. If the result is a positive multiple of a vector, it is parallel to it and the angle is zero.
Answer from the NTA final answer key. Solution by PrepWiser.