(Solved): 1. Determine which, if any, vector is perpendicular to v=2,2,1. w=5,4,2,u=3 ...

1. Determine which, if any, vector is perpendicular to $\mathbf{v}=??2,?2,1?$. $\mathbf{w}=?5,?4,2?,\mathbf{u}=?3,?1,8?$ 2. Consider the point $(5,0,?1)$ and the vector $\mathbf{v}=??2,?2,1?$ (a) Find the parametric equations of the line through the point and parallel to $\mathbf{v}$. (b) Fine the symmetric equation of this line. (c) Find the distance from this line to the origin $(0,0,0)$. (Hard?) 3. Consider the plane given by $2x?3y+2z=2$ (a) Show that the line given by $\frac{x?1}{4}=\frac{y?2}{2}=\frac{z?3}{?1}$ is contained in the plane. (b) Find another line in the plane perpendicular to the line in part a.