Mathematics

Problem

Let

P(2,-1,4)

Q(6,3,-2)

and

R(-1,5,1)

be three points in space. Answer the following: a. (i) Find the vectors

\overrightarrow{PQ}

and

\overrightarrow{PR}

in component form. b. (ii) Determine the vector that must be added to

\overrightarrow{PQ}

so that the sum equals

\overrightarrow{PR}

. c. (iii) By drawing a neat sketch of triangle

PQR

with the vectors placed tail-to-head, verify graphically the relation obtained in part (ii).