Mathematics

Problem

Two vectors are given by

\mathbf{u}=\langle 4,-1,2\rangle

and

\mathbf{v}=\langle -3,5,1\rangle

. a. (i) Calculate

|\mathbf{u}|

and

|\mathbf{v}|

. b. (ii) Find

\mathbf{u}\cdot\mathbf{v}

. c. (iii) Determine the angle between

\mathbf{u}

and

\mathbf{v}

, correct to one decimal place. d. (iv) State whether the angle obtained in part (iii) is acute or obtuse.