Question

If a line lies in the octant OXYZ and it makes equal angles with the axes, then ______.

Options

• `l = "m" = "n" = 1/sqrt(3)`

• `l = "m" = "n" = +- 1/sqrt(3)`

• `l = "m" = "n" = -1/sqrt(3)`

• `l = "m" = "n" = +- 1/sqrt(2)`

Answer 1

If a line lies in the octant OXYZ and it makes equal angles with the axes, then `l = "m" = "n" = +- 1/sqrt(3)`.

Explanation:

Since, `cos^2alpha + cos^2beta + cos^2ϒ` = 1

∴ `cos^2alpha + cos^2alpha + cos^2alpha` = 1   .....`(alpha = beta = ϒ)`

⇒ `3 cos^2alpha` = 1

⇒ `cos^2alpha = 1/3`

⇒ `cos alpha = +- 1/sqrt(3)`

Now, `l = "m" = "n" = cos alpha`

∴  `l = "m" = "n" = +- 1/sqrt(3)`