Question 1040746
Let O be the origin (0,0,0).
Then vector OA = <3,0,2>,
vector OB = <2,-2,5>,
vector OC = <0,2,7>, and 
vector OD = <-2,10,7>.

(i)
==> BA = OA - OB = <1,2,-3>.  Also,

BC = OC - OB = <-2,4,2> = 2<-1,2,1>.

==>BA*BC = 1*-2 + 2*4 + -3*2 = -2+8-6 = 0.

==> Vectors BA and BC are perpendicular.


(ii)
Now AD = OD - OA = <-5,10,5> = 5<-1,2,1>.
Since both BC and AD are non-zero multiples of the same vector <-1,2,1>,  these two vectors are parallel.

==> {{{abs(BC)/abs(AD) = 2/5}}}.