Determine whether the point \(( 19 , - 12,17 )\) lies on the line \(\mathbf { r } = \left( \begin{array} { r } 4 - 2 7 \end{array} \right) + \lambda \left( \begin{array} { r } 3 - 2 4 \end{array} \right)\).
Vectors \(\mathbf { a }\) and \(\mathbf { b }\) are given by \(\mathbf { a } = \left( \begin{array} { r } 1 - 2 2 \end{array} \right)\) and \(\mathbf { b } = \left( \begin{array} { r } - 3 6 2 \end{array} \right)\).
Find, in degrees, the angle between \(\mathbf { a }\) and \(\mathbf { b }\).
Find a vector which is perpendicular to both \(\mathbf { a }\) and \(\mathbf { b }\).