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MathsJEE Main 23 Jan 2026, Shift 2·Q3·MCQ·Easy–moderate

Vectors · Cross product and projection

Let a⃗=i^−2j^+3k^\vec a = \hat i - 2\hat j + 3\hat k, b⃗=2i^+j^−k^\vec b = 2\hat i + \hat j - \hat k, c⃗=λi^+j^+k^\vec c = \lambda\hat i + \hat j + \hat k and v⃗=a⃗×b⃗\vec v = \vec a\times\vec b. If v⃗⋅c⃗=11\vec v\cdot\vec c = 11 and the length of the projection of b⃗\vec b on c⃗\vec c is pp, then 9p29p^2 is equal to:
  1. (1)9
  2. (2)6
  3. (3)4
  4. (4)12

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