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

• A

  $\left(0, \frac{1}{2}, \frac{1}{\sqrt{2}}\right)$
• Correct answer
  B

  $\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
• C

  $\left(1, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
• D

  $\left(1, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

Hence, the correct answer is option: 'B'.