Mathematics

Problem

In three–dimensional space consider the points

P(3,-1,4)

and

Q(-5,6,4)

. (i) Verify that both points lie in the same plane parallel to the

xy

-plane. (ii) Find the length of segment

PQ

. (iii) A point

R(k,2k,4)

also lies in the same plane. Determine all real values of

k

for which

R

is equidistant from

P

and

Q

. (iv) Using your result from part (iii), compute the common distance

PR=QR

for each admissible value of

k