Question

Find the direction cosine of a line which makes equal angle with coordinate axes.

Options

• `+- 1/sqrt(3), +- 1/sqrt(3), +- 1/sqrt(3)`

• `- 1/sqrt(3), 1/sqrt(3), 1/sqrt(3)`

• `- 1/sqrt(3), -1/sqrt(3), -1/sqrt(3)`

• None of the above

Answer 1

`+- 1/sqrt(3), +- 1/sqrt(3), +- 1/sqrt(3)`

Explanation:

Let direction angle be a each.

∴ Direction cosines and cosa, cosa, cosa

But `l^2 + m^2 + n^2` = 1, where 1, m, n are the direction cosines of the line.

∴ `cos^2 alpha + cos^2 alpha + cos^2 alpha` = 1

`3 cos^2 alpha` = 1

∴ `cos alpha = 1/sqrt(3)`

As a result, the direction cosine of the line parallel to the coordinate axes is `+- 1/sqrt(3), +- 1/sqrt(3), +- 1/sqrt(3)`.