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MathsJEE Main 22 Jan 2026, Shift 1·Q1·MCQ·Moderate

Vectors · Projection of a vector

Let AB→=2i^+4j^−5k^\overrightarrow{AB} = 2\hat i + 4\hat j - 5\hat k and AD→=i^+2j^+λk^\overrightarrow{AD} = \hat i + 2\hat j + \lambda\hat k, λ∈R\lambda \in \mathbb{R}. Let the projection of the vector v⃗=i^+j^+k^\vec v = \hat i + \hat j + \hat k on the diagonal AC→\overrightarrow{AC} of the parallelogram ABCDABCD be of length one unit. If α,β\alpha, \beta, where α>β\alpha > \beta, be the roots of the equation λ2x2−6λx+5=0\lambda^2x^2 - 6\lambda x + 5 = 0, then 2α−β2\alpha - \beta is equal to
  1. (1)1
  2. (2)4
  3. (3)3
  4. (4)6
We corrected a printing error in the original paper

Source printed “2i^+4j^−5k2\hat i + 4\hat j - 5k” and “i^+2j^+λk\hat i + 2\hat j + \lambda k” (unit vector k^\hat k printed without its hat).

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See the full 22 Jan 2026, Shift 1 paper

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