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The angle between vector ⃗Q and the resultant of (2⃗Q + 2⃗P) and (2⃗Q - 2⃗P) is

Asked in JEE Main 5th April 1st Shift 2024 · Vector subtraction

(1) 0°
(2) tan⁻¹((2Q - 2P))/(2Q + 2P)
(3) tan⁻¹((2Q)/P)
(4) tan⁻¹(/PQ)

Answer: (1) 0°

Step-by-step solution

Resultant = (2⃗Q + 2⃗P) + (2⃗Q - 2⃗P) = 4⃗Q.

It is a positive multiple of ⃗Q, so the angle with ⃗Q is 0°.

Why the other options are wrong

(2) Treats the two given vectors as perpendicular components of the resultant; they are not, and their ⃗P parts cancel.
(3) No single slip gives this; the ⃗P parts cancel exactly, leaving a vector along ⃗Q.
(4) Treats ⃗P and ⃗Q as perpendicular components of the resultant, but the ⃗P parts cancel.

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