Mathematics

Problem

The points

A(2,-1,4)

and

B(5,3,-2)

are given in space. (i) Obtain the vector

\vec{AB}

. (ii) Find the unit vector along

\vec{AB}

, expressing your answer in simplest radical form. (iii) If a vector

\vec{u}

is parallel to

\vec{AB}

and has magnitude

7

units, determine

\vec{u}