Question

Show that no line in space can make angle and with X- axis and Y-axis.

Answer 1

Let, if possible, a line in space make angles and with X-axis and Y-axis.

Let the line make angle \(\gamma\) with Z-axis.

This is not possible, because cos γ is real

∴ cos²γ cannot be negative.

Hence, there is no line in space which makes angles and with X-axis and Y-axis.