Q. 14.2( 25 Votes )

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.

Answer :

Let us assume the angles that made with the positive direction of x, y, and z-axes be ,, .


Then we get,





We know that if a line makes angles of with the positive x, y, and z-axes then the direction cosines of that line is the cosine of that angles made by that line with the axes.


Let us assume that l, m, n are the direction cosines of the line. Then,





We substitute the values of in the above equations for the values of l, m, n.








The direction cosines of the given line is .

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