If a line makes an angle of 60°, 135°, 120° with the positive x, y, z-axis, respectively, then find the direction cosines.

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  1. \(\rm l=\frac{1}{2},m=-\frac{1}{\sqrt2}, n=-\frac{1}{2}\)
  2. \(\rm l=-\frac{1}{2},m=\frac{1}{\sqrt2}, n=-\frac{1}{2}\)
  3. \(\rm l=-\frac{1}{2},m=-\frac{1}{\sqrt2}, n=-\frac{1}{2}\)
  4. \(\rm l=\frac{1}{2},m=\frac{1}{\sqrt2}, n=-\frac{1}{2}\)

Answer (Detailed Solution Below)

Option 1 : \(\rm l=\frac{1}{2},m=-\frac{1}{\sqrt2}, n=-\frac{1}{2}\)
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Detailed Solution

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Concept:

If a line makes an angle of α, β, and γ with the positive x, y, and z-axis, respectively, then the direction cosines of the line are cos α, cos β, cos γ.

Calculation:

Given, a line makes an angle of 60°, 135°, 120° with the positive x, y, z-axis, respectively, 

⇒ The direction cosines of the line are (l, m, n) = (cos 60°, cos 135°, cos 120°)

⇒ \(\rm l=\frac{1}{2},m=-\frac{1}{\sqrt2}, n=-\frac{1}{2}\)

∴ The correct option is (1).

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