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MathsJEE Main 2 Apr 2026, Shift 2·Q14·MCQ·Easy–moderate

Vectors · Dot product and linear combination

Let the vectors a⃗=−i^+j^+3k^\vec a = -\hat i + \hat j + 3\hat k and b⃗=i^+3j^+k^\vec b = \hat i + 3\hat j + \hat k. For some λ,μ∈R\lambda, \mu \in \mathbb{R}, let c⃗=λa⃗+μb⃗\vec c = \lambda\vec a + \mu\vec b. If c⃗⋅(3i^−6j^+2k^)=10\vec c\cdot(3\hat i - 6\hat j + 2\hat k) = 10 and c⃗⋅(i^+j^+k^)=−2\vec c\cdot(\hat i + \hat j + \hat k) = -2, then ∣c⃗∣2\lvert\vec c\rvert^2 is equal to:
  1. (1)8
  2. (2)12
  3. (3)14
  4. (4)15

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