Find the values of p so that the lines $\frac{ \large 1 - x }{ \large 3} = \frac{ \large 7y - 14}{ \large 2p} = \frac{ \large z - 3}{ \large 2}\: and \: \frac{ \large 7 - 7x }{ \large 3 \: p} = \frac{ \large y - 5}{ \large 1} = \frac{ \large 6 - z}{ \large 5}$ are at right angles.

Question

$\begin{array}{1 1} p=\frac{70}{11} \\ p=\frac{-10}{11} \\ p=\frac{10}{7} \\p=\frac{11}{70} \end{array}$