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MathsJEE Main 23 Jan 2026, Shift 2·Q10·MCQ·Moderate

Vectors · Vector cross product equations

Let a⃗,b⃗,c⃗\vec a, \vec b, \vec c be three vectors such that a⃗×b⃗=2(a⃗×c⃗)\vec a\times\vec b = 2(\vec a\times\vec c). If ∣a⃗∣=1\lvert\vec a\rvert = 1, ∣b⃗∣=4\lvert\vec b\rvert = 4, ∣c⃗∣=2\lvert\vec c\rvert = 2, and the angle between b⃗\vec b and c⃗\vec c is 60∘60^\circ, then ∣a⃗⋅c⃗∣\lvert\vec a\cdot\vec c\rvert is:
  1. (1)2
  2. (2)4
  3. (3)0
  4. (4)1

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