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MathsJEE Main 24 Jan 2026, Shift 1·Q5·MCQ·Easy–moderate

Vectors · Cross product and dot product

Let a⃗=2i^+j^−2k^\vec a = 2\hat i + \hat j - 2\hat k, b⃗=i^+j^\vec b = \hat i + \hat j and c⃗=a⃗×b⃗\vec c = \vec a \times \vec b. Let d⃗\vec d be a vector such that ∣d⃗−a⃗∣=11\lvert\vec d - \vec a\rvert = \sqrt{11}, ∣c⃗×d⃗∣=3\lvert\vec c \times \vec d\rvert = 3 and the angle between c⃗\vec c and d⃗\vec d is π4\dfrac{\pi}{4}. Then a⃗⋅d⃗\vec a \cdot \vec d is equal to
  1. (1)11
  2. (2)3
  3. (3)0
  4. (4)1

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