Homework Statement
Homework Equations
dot product a.b = lal.lblcostheta
vectors are perpendicular when a.b = 0
The Attempt at a Solution
OA . LA = 0
OA = OM + MA
LA = LO + OA
OA . LA = (OM+MA) . (LO + OA)
= OM.LO + OM.OA + MA.LO + MA.OAi get stuck here
Homework Statement
In the following diagram D and E are the midpoints of AB and AC. Use vector methods to prove that DE = 1/2BC
Homework Equations
DE = 1/2 BC
The Attempt at a Solution
AD = 1/2AB
AE = 1/2AC
AD + DE = AE
DE = -AE + AD
DE = -1/2AC + 1/2AD
IF BC = -AC + AB
AND DE = -1/2AC +...
Homework Statement
The diagonals of quadrilateral ABCD bisect each other. Use vectors to prove that ABCD is a parallelogram.
The Attempt at a Solution
let O = point of intersection
AO = AD + DO
DO = 1/2DB
AO = AD + 1/2 DB
AO = AB + BO
BO = -1/2DB
AO = AB - 1/2DB
2AO = AD...
Homework Statement
If OA = 1/3OB + 2/3OC, then prove that A, B, and C are collinear and that A divides the segment BC in the ratio 2:1.
Homework Equations
OA = 1/3 OB + 2/3OC
A divides segment BC into 2/3s
The Attempt at a Solution
I don't know where to start on this...