Mathematics

Problem

The vectors

\mathbf{a}=\langle 2,\,t,\,6\rangle

and

\mathbf{b}=\langle 1,\,3,\,4\rangle

depend on the real parameter

t

. a. (i) Find the value of

t

for which

\mathbf{a}

is parallel to

\mathbf{b}

. b. (ii) Find the value of

t

for which

\mathbf{a}

is perpendicular to

\mathbf{b}

. c. (iii) For each value of

t

obtained in parts (i) and (ii), compute

|\mathbf{a}|^{2}

and state what the result represents geometrically for the corresponding vector

\mathbf{a}