Let and . Answer the following…

MATHEMATICS · Multi-part · A Level · Mathematics · Vectors · Vectors

Problem

Let

\vec{a}=3\mathbf{i}-2\mathbf{j}+6\mathbf{k}

and

\vec{b}=4\mathbf{i}+5\mathbf{j}-2\mathbf{k}

. Answer the following questions. (i) Find the magnitudes

|\vec{a}|

and

|\vec{b}|

. (ii) Calculate the angle between

\vec{a}

and

\vec{b}

, giving your answer correct to the nearest degree. (iii) State whether this angle is acute or obtuse and give a brief reason for your answer.