The angle which the line x/1 = y/(-1) = z/0 makes with the positive d…

The correct answer is Option (2) → $\frac{3\pi}{4}$ ##

Given line is

$\frac{x}{1} = \frac{y}{-1} = \frac{z}{0}$

$∴$ Direction ratios of line are: $1, -1, 0$

We know that direction ratio of y-axis are $0, 1, 0$

$\cos\theta = \left| \frac{\vec{b_1} \cdot \vec{b_2}}{|\vec{b_1}| \cdot |\vec{b_2}|} \right|$

$= \frac{(\hat{i} - \hat{j}) \cdot (\hat{j})}{\sqrt{(1)^2 + (-1)^2} \sqrt{(1)^2}} \quad [∵\vec{b_1} = \hat{i} - \hat{j} \text{ and } \vec{b_2} = \hat{j}]$

$= \frac{-1}{\sqrt{2}}$

$\cos\theta = \cos\left(\frac{3\pi}{4}\right)$

$\Rightarrow \theta = \frac{3\pi}{4}$