Mathematics

Problem

(Distance expressed in terms of a parameter) a. (i) Let

P(t,1,2)

and

Q(4,4,6)

be two points, where

t

is a real parameter. Obtain an expression for

PQ^{2}

in terms of

t

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

t

for which

PQ

equals

5

units. c. (iii) How many distinct points

P

satisfy the condition obtained in part (ii)? Justify your answer.