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JEE Main 2022Mathematics Vectors & 3D Geometry

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mcq
2022
Official previous-year question

Verified 30 May 2026.

Question

The direction cosines of the line joining points $(1,2,3)$ and $(4,6,3)$ are:

Options

  1. A

    $\frac{3}{5}, \frac{4}{5}, 0$

  2. B

    $\frac{3}{5}, \frac{4}{5}, \frac{1}{5}$

  3. C

    $\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0$

  4. D

    $\frac{1}{3}, \frac{2}{3}, 0$

Solution

Direction ratios: $(4-1, 6-2, 3-3) = (3, 4, 0)$

$|DR| = \sqrt{9+16+0} = 5$

Direction cosines: $\frac{3}{5}, \frac{4}{5}, 0$

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