Finding Perpendicular Vector, Help!!!

I really need help on vectors were you have to find a perpendicular vector. I have 2 questons that are really confusing me:

1. Find a vector which is perpendicular to both a and b

a = $\displaystyle (i+3j-k)$

b = $\displaystyle (3i-j-k)$

2. Show that lines L1 and L2 are perpendicular to each other.

L1: $\displaystyle r = \left(\begin{array}{c}5\\3\\0\end{array}\right) + \lambda \left(\begin{array}{c}-7\\-7\\7\end{array}\right)$

L2: $\displaystyle r = \left(\begin{array}{c}1\\-3\\-4\end{array}\right) + \mu \left(\begin{array}{c}1\\2\\3\end{array}\right)$

Thank You, this part of vectors is really confusing me