Find the acute angle which the line with direction cosinesn makes with the positive direction ofz-axis.

OR

Find the direction cosines of the line:

If (l, m, n) are direction cosines of a line then we know that,

l² + m² + n² = 1

Given direction cosines

So,

As, we need to find an acute angle so we will take positive value of n, hence

⇒ γ = 45˚

OR

Given line,

If, l, m, n are direction cosines of a line and a, b, c are its direction ratio’s then we know that,

respectively.

Direction ratios of given line = 2, -1, 2

Therefore, the direction cosines of the given line are