Question
Find the direction-cosines of a line which makes equal angles with the axes. How many such lines are there?
Solution
Let α be the angle which the line with all the axes,
∴ its direction-cosines are cos α, cos α, cos α
required direction-cosines are 
These are four different groups of signs
i.e., +, +, +
+, -, +
+, +, -
+, -, -
∴ there are four distinct lines.
∴ its direction-cosines are cos α, cos α, cos α
required direction-cosines are These are four different groups of signs
i.e., +, +, +
+, -, +
+, +, -
+, -, -
∴ there are four distinct lines.
