Given, the direction ratios of the line are proportional to (0, 1, -1)
Therefore, consider the direction ratios of the give line can be
a = 0 × k, b = 1 × k, c = (-1) × k
[where k is some proportionality constant]
Now the direction ratios of the line are
a = 0, b = k, c = -k
As we know the direction cosine of z-axis can be given by
cos γ = n = \(\frac{c}{\sqrt{a^2+b^2+c^2}}\) where γ is the angle made by the line with the z-axis.
By using the above formula:
[As cosine function is negative, the angle become 135° instead of 45°]
\(\gamma = \frac{3\pi}{4}\)
The inclination of the line with z-axis is \(\frac{3\pi}{4}\)
