Q41 / 160 · AP EAMCET 2020 (17 Sep Shift 2) · Mathematics

If a line makes angles \(90^{\circ}, 135^{\circ}\) and \(45^{\circ}\) with the positive directions of \(X, Y, Z\)-axes respectively. Then, its direction cosines are

  • Correct answer
    A
    \(\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
  • B
    \(\left(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
  • C
    \(\left(0, \frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
  • D
    \(\left(0, \frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)

Solution

Given angles made by line with axes are \(\alpha=90^{\circ}, \quad \beta=135^{\circ}, \quad \gamma=45^{\circ}\) So, direction cosines are, \(\begin{aligned} & \cos \alpha=\cos 90^{\circ}=0 \\ & \cos \beta=\cos 135^{\circ}=-\frac{1}{\sqrt{2}} \\ & \cos \gamma=\cos 45^{\circ}=\frac{1}{\sqrt{2}} \end{aligned}\)

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

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