Find the direction cosines of a line which makes equal angles with the coordinate axes.

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Solution

It is given that the line makes equal angles with the coordinate axis. The angle made be the line is α with respect to x-axis, y-axis and z-axis.

Let the direction cosine of the line be l,m,n. Then,

l=cosα m=cosα n=cosα

We know that l 2 + m 2 + n 2 =1.

Substitute the value of l, m and n in the above formula.

cos 2 α+ cos 2 α+ cos 2 α=1 3 cos 2 α= 1 3 cosα=± 1 3

Thus, the direction cosines are ± 1 3 ,± 1 3 and ± 1 3 .

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