JPJC Vectors Tutorial 1(a) Q1

The vectors \({\mathbf{a}}\), \({\mathbf{b}}\) and \({\mathbf{c}}\) are given by \(\mathbf{a}=3\mathbf{i}+4\mathbf{j}+5\mathbf{k}\), \(\mathbf{b}=-\mathbf{i}+\mathbf{j}-\mathbf{k}\), \(\mathbf{c}=2\mathbf{i}-\mathbf{j}+2\mathbf{k}\) respectively.

1. Find the unit vector in the direction of \({\mathbf{a}}\).[1]
2. Find the unit vectors parallel to \({\mathbf{b}}\).[2]
3. Find the angle between the vectors \({\mathbf{b}}\) and \({\mathbf{c}}\), giving your answer to the nearest \(0.1{}^\circ \).[2]
4. Find the vector of magnitude \(5\) in the direction of \({\mathbf{c}}\).[2]