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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

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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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