Target Exam

CUET

Subject

Section B1

Chapter

Three-dimensional Geometry

Question:

If a line has direction ratios $2, -1, -2$, determine its direction cosines.

Options:

$(\frac{2}{3}, -\frac{1}{3}, -\frac{2}{3})$

$(\frac{2}{3}, \frac{1}{3}, \frac{2}{3})$

$(2, -1, -2)$

$(\frac{1}{3}, -\frac{2}{3}, -\frac{2}{3})$

Correct Answer:

$(\frac{2}{3}, -\frac{1}{3}, -\frac{2}{3})$

Explanation:

The correct answer is Option (1) → $(\frac{2}{3}, -\frac{1}{3}, -\frac{2}{3})$ ##

Direction cosines are

$\frac{2}{\sqrt{2^2 + (-1)^2 + (-2)^2}}, \frac{-1}{\sqrt{2^2 + (-1)^2 + (-2)^2}}, \frac{-2}{\sqrt{2^2 + (-1)^2 + (-2)^2}}$

Or $\frac{2}{3}, -\frac{1}{3}, -\frac{2}{3}$.