1003164406

Determine whether any of the lines \( p \), \( q \) or \( r \) defined by the parametric equations given below passes through the coordinate origin. \begin{align*} p\colon x&=-2+4t, & q\colon x&=-5-5s, & r\colon x&=3-6u, \\ y&=1-2t, & y&=2-2s, & y&=-\frac12+u, \\ z&=-3+3t;\ t\in\mathbb R & z&=5+5s;\ s\in \mathbb R & z&=2-4u;\ u\in \mathbb R \end{align*}