Mathematics

Problem

(a) Define a unit vector and write its general mathematical expression in terms of an arbitrary vector

\mathbf{A}

. (b) A displacement vector is given by

\mathbf{P}=3\,\hat{i}-4\,\hat{j}+12\,\hat{k}

. Show, by explicit calculation, that the vector

\hat{p}=\dfrac{\mathbf{P}}{|\mathbf{P}|}

has unit magnitude.