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# Solution for If a Line Makes Angles of 90°, 60° and 30° with the Positive Direction Of X, Y, And Z-axis Respectively, Find Its Direction Cosines - CBSE (Commerce) Class 12 - Mathematics

ConceptDirection Cosines and Direction Ratios of a Line

#### Question

If a line makes angles of 90°, 60° and 30° with the positive direction of xy, and z-axis respectively, find its direction cosines

#### Solution 1

Let the direction cosines of the line be l, m, n.

Now,

$l = \cos {90}^0 = 0$

$m = \cos {60}^0 = \frac{1}{2}$

$n = \cos {30}^0 = \frac{\sqrt{3}}{2}$

$\text{Therefore, the direction cosines of the line are }0, \frac{1}{2}, \frac{\sqrt{3}}{2} .$

#### Solution 2

Let the direction cosines of the line be l, m, n.

Now,

$l = \cos {90}^0 = 0$

$m = \cos {60}^0 = \frac{1}{2}$

$n = \cos {30}^0 = \frac{\sqrt{3}}{2}$

$\text{Therefore, the direction cosines of the line are }0, \frac{1}{2}, \frac{\sqrt{3}}{2} .$

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Solution If a Line Makes Angles of 90°, 60° and 30° with the Positive Direction Of X, Y, And Z-axis Respectively, Find Its Direction Cosines Concept: Direction Cosines and Direction Ratios of a Line.
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