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Jee Main 2025 — Medium JEE math MCQ

Let \(\mathbf{a} = 3\mathbf{i} - \mathbf{j} + 2\mathbf{k}, \mathbf{b} = \mathbf{a} \times (\mathbf{i} - 2\mathbf{k})\) and \(\mathbf{c} = \mathbf{b} \times \mathbf{k}\). Then the projection of \(\mathbf{c} - 2\mathbf{j}\) on \(\mathbf{a}\) is
  1. A. \(2\sqrt{14}\)
  2. B. \(\mathbf{v}\)
  3. C. \(\sqrt{7}\)
  4. D. \(2\sqrt{7}\)

Solution

The correct option is **A**. (A. \(2\sqrt{14}\))

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let a=3i−j+2k,b=a×(i−2k)\mathbf{a} = 3\mathbf{i} - \mathbf{j} + 2\mathbf{k}, \mathbf{b} = \mathbf{a} \times (\mathbf{i} - 2\mathbf{k}) and c=b×k\mathbf{c} = \mathbf{b} \times \mathbf{k}. Then the projection of c−2j\mathbf{c} - 2\mathbf{j} on a\mathbf{a} is
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep