Question

Find the direction cosines of the line and the angles made by the line with the coordi-
nate axes if the direction ratios of the line are (-6,2, 3).
​

Answer 1

Step-by-step explanation:

Let the direction cosines of the line make an angle a with each of the coordinate axes.

∴ l=cosa,m=cosa,n=cosa

We know l

2

+m

2

+n

2

=1

⇒ cos

2

α+cos

2

α+cos

2

α=1

⇒ 3cos

2

α=1

⇒ cos

2

α=

3

1

⇒ cosα=±

3

1

Thus, the direction cosines of the line which is equally inclined to the coordinate axes are ±

3

1

,±

3

1

and ±

3

1

.

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