A line L1 passes through point A, with position vector $\displaystyle 5i + 3j$, and the point B, with position vector $\displaystyle -2i -4j +7k$.

a) Write down equation for line L1

i got the equation of line L1 as: $\displaystyle r = a + \lambda[(b-a)] $ :

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

A second line L2 has equation: $\displaystyle r = i - 3j - 4k + \mu(i + 2j + 3k)$

b) Show that L1 and L2 are perpendicular to each other.

c) Show that the two lines meet, and find the position vector of th epoint of inersection.

I need help with parts (b) and (c) assuming my part (a) is correct.

Thank You