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A line passes through the point with position vector 2 i - j + 4 k and is in the direction of the vector i + j - 2 k. The equation of the line in…

CUET UG 2025 — Mathematics Geometry

2025mcqmedium

A line passes through the point with position vector 2i^−j^+4k^2\hat{i} - \hat{j} + 4\hat{k}2i^−j^​+4k^ and is in the direction of the vector i^+j^−2k^\hat{i} + \hat{j} - 2\hat{k}i^+j^​−2k^. The equation of the line in Cartesian form is:

Official previous-year question

Held on 26 May 2025 · Verified 13 Jul 2026.

Options

  1. A

    x−21=y+11=4−z2\frac{x-2}{1} = \frac{y+1}{1} = \frac{4-z}{2}1x−2​=1y+1​=24−z​

  2. B

    x+21=y−11=z−42\frac{x+2}{1} = \frac{y-1}{1} = \frac{z-4}{2}1x+2​=1y−1​=2z−4​

  3. C

    x−21=y−11=z−42\frac{x-2}{1} = \frac{y-1}{1} = \frac{z-4}{2}1x−2​=1y−1​=2z−4​

  4. D

    x−21=y+11=z−42\frac{x-2}{1} = \frac{y+1}{1} = \frac{z-4}{2}1x−2​=1y+1​=2z−4​

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