If a line makes angles $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive $X, Y$ and $Z$ axis…

If a line makes angles $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive $X, Y$ and $Z$ axis respectively, then its direction cosines are
  1. $\left(0, \frac{1}{2}, \frac{1}{\sqrt{2}}\right)$
  2. $\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
  3. $\left(1, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
  4. $\left(1, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

Solution

Given, a line makes $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive $x, y$ and $z$ axes respectively. Hence, it's direction cosines are $ < \cos 90^{\circ}, \cos 135^{\circ}, \cos 45^{\circ}>$ $=\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

Asked in: AP EAMCET 2021 (23 Aug Shift 2)

Practice more Three Dimensional Geometry questions on Aicharya