Answers

2015-09-24T21:45:39+05:30
If the line is equally inclined to all the coordinate axes, let it be inclined at α.

So the direction cosines are:
l = cos α
m = cos α
n = cos α

We know that l² + m² + n² = 1
⇒ cos² α + cos² α + cos² α = 1
⇒ 3cos² α = 1
⇒ cos² α = 1/3
⇒ cos α = \pm  \frac{1}{ \sqrt{3} }

So the direction cosines are ( \frac{1}{ \sqrt{3}},  \frac{1}{ \sqrt{3}},  \frac{1}{ \sqrt{3} } ) and (- \frac{1}{ \sqrt{3}},- \frac{1}{ \sqrt{3}},- \frac{1}{ \sqrt{3}})
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