SOLUTION: a rectangle labeled abcd counter clockwise. point E lies on the diagonal ac such that ae:ac is 4:5. point f lies on the midpoint of cd. express ef in terms of the position vectors

Algebra ->  Parallelograms -> SOLUTION: a rectangle labeled abcd counter clockwise. point E lies on the diagonal ac such that ae:ac is 4:5. point f lies on the midpoint of cd. express ef in terms of the position vectors       Log On


   

Question 1008551: a rectangle labeled abcd counter clockwise. point E lies on the diagonal ac such that ae:ac is 4:5. point f lies on the midpoint of cd. express ef in terms of the position vectors oa, ob, oc, and od
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
AE%2FAC=4%2F5
.
.
.
OD%2B%281%2F2%29%28DC%29=OA%2BAE%2BEF
or
EF=OD-OA%2B%281%2F2%29%28DC%29-AE
Substituting from above,
EF=OD-OA%2B%281%2F2%29%28DC%29-%284%2F5%29AC
But you know that
OA%2BAC=OC
AC=OC-OA
So,
EF=OD-OA%2B%281%2F2%29%28DC%29-%284%2F5%29%28OC-OA%29
and,
OD%2BDC=OC
DC=OC-OD
So,
EF=OD-OA%2B%281%2F2%29%28OC-OD%29-%284%2F5%29%28OC-OA%29
EF=OD-OA%2B%281%2F2%29%28OC%29-%281%2F2%29%28OD%29-%284%2F5%29%28OC%29%2B%284%2F5%29OA%29
EF=%281%2F2%29OD-%281%2F5%29OA-%283%2F10%29%28OC%29%29