Mathematics

Problem

(a) Define a unit vector and write its usual symbolic representation. (b) Let

\vec{a}=a\mathbf{i}+b\mathbf{j}+c\mathbf{k}

be any non-zero vector. Prove that the vector

\hat{a}=\dfrac{\vec{a}}{|\vec{a}|}

has magnitude

1

. (c) Show that the direction cosines of

\hat{a}

are the same as those of

\vec{a}