The points AAA, B B\,B and C C\,C have position vectors
a=2i−j+3k\mathbf{a} = 2\mathbf{i} - \mathbf{j} + 3\mathbf{k}a=2i−j+3k, b=5i+2j−k\mathbf{b} = 5\mathbf{i} + 2\mathbf{j} - \mathbf{k}b=5i+2j−k, c=i+4j+3k\mathbf{c} = \mathbf{i} + 4\mathbf{j} + 3\mathbf{k}c=i+4j+3k
Find the position vector of the midpoint M M\,M of BCBCBC.
Find ∣AM⃗∣\left|\vec{AM}\right|AM, giving your answer in exact form.