Mathematics

Problem

Let the vectors be

\displaystyle \mathbf{p}=\langle t,2t,3\rangle

\mathbf{q}=\langle 1,-t,6\rangle

and

\mathbf{r}=\langle 2,t^{2},0\rangle

, where

t

is a real parameter. a. (i) Determine all value(s) of

t

for which

\mathbf{p}

is perpendicular to

\mathbf{q}

. b. (ii) For the value(s) of

t

obtained in part (i), examine whether

\mathbf{q}

is perpendicular to

\mathbf{r}

and justify your conclusion. c. (iii) Find all real value(s) of

t

for which the three vectors

\mathbf{p},\;\mathbf{q}

and

\mathbf{r}

are pairwise perpendicular.