C4 Vector question help please !

ABCD is a parallelogram. The position vectors of A,B and C are given respectively by

a= 2i + j + 3k

b= 3i - 2j

c= i - j - 2k

a)find the position vector of D
b) Determine to the nearest degree , the angle ABC

thanks in advance guys.

Reply 1

Rabite

BC=AD (parallelogram) = C-B
So add C-B to A to get D, I guess.

For angle ABC, you need to get the vector BA=A-B and BC=C-B.
Then do (A-B)dot(C-B) / (|A-B||C-B|) and de-Cosine it. (Definition of the dot product)

Reply 2

rayman198

Can anyone confirm thats correct please? (no offence rabite lol, its just u didnt sound 2 sure)

Reply 3

britman2k2

If Parallelogram AB = CD

AB = OB - OA
= (3,-2,0) - (2,1,3)
=(1,-3,-3)

CD = OD - OC
so,
OD = CD + OC
= (1,-3,-3) + (1,-1,-2)
= (2,-4,-5)

How about that??