1. **Problem 1:** Consider vectors $\vec{A}$ and $\vec{B}$ with an angle $\theta$ between them where $0 \leq \theta \leq \pi$. We need to identify the nature of the angle $\theta$ based on the options: a) parallel, b) perpendicular, c) obtuse. - Two vectors are **parallel** if $\theta = 0$ or $\theta = \pi$. - They are **perpendicular** if $\theta = \frac{\pi}{2}$. - They are **obtuse** if $\frac{\pi}{2} < \theta < \pi$. 2. **Problem 2:** For the line $y = mx + c$, given a point $(x_1, y_1)$ on the line, find the expression for the $y$-coordinate when $x = x_2$. - The line equation is $y = mx + c$. - Since $(x_1, y_1)$ lies on the line, $y_1 = m x_1 + c$. - To find $y$ at $x = x_2$, substitute $x_2$ into the line equation: $y_2 = m x_2 + c$. - Using $c = y_1 - m x_1$, we get: $$y_2 = m x_2 + y_1 - m x_1 = y_1 + m (x_2 - x_1)$$ - The $y$-coordinate difference is: $$y_2 - y_1 = m (x_2 - x_1)$$ - Among the options, the expression $y_2 - y_1$ corresponds to the difference in $y$-coordinates. **Final answers:** - Q1: The angle $\theta$ can be parallel, perpendicular, or obtuse depending on its value in $[0, \pi]$. - Q2: The $y$-coordinate difference is $y_2 - y_1$ (option a).