Mathematics

Problem

Let the position vectors of points

A(2,-1,4)

and

B(-3,5,1)

with respect to the origin be

\mathbf{a}

and

\mathbf{b}

respectively. a. (i) Find the vectors

\mathbf{a}

and

\mathbf{b}

in component form. b. (ii) Calculate the exact value of the angle

\angle AOB

between

\mathbf{a}

and

\mathbf{b}

, where

O

is the origin. c. (iii) State whether the angle obtained in part (ii) is acute, right or obtuse, giving a reason based on your calculation.