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GATE 2023 MN – Question 14

Engineering Mathematics · Vector Calculus · 1 mark · Multiple choice

Given $\mathbf A=3\mathbf i+2\mathbf j$ and $\mathbf B=\mathbf i+\mathbf j$, find the magnitude of the projection of A along B.

  1. $5/\sqrt2$
  2. $5/\sqrt{13}$
  3. $5/\sqrt{26}$
  4. 5

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Correct answer: (A) $5/\sqrt2$

Explanation

The scalar projection is $|\mathbf A\cdot\mathbf B|/|\mathbf B|$. Here the dot product is 3+2 = 5 and the magnitude of B is √2. The result is 5/√2, A. Dividing by the magnitude of A would project in the opposite direction.

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