ABCD is a parallelogram and P is the point of intersection of its diagonals,if O is the origin of reference, show that OA vector+OB vector+OC vector+OD vector=4OP vector
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Step-by-step explanation:
ANSWER
OA
+
OB
+
OC
+
OD
=(
OP
+
PA
)+(
OP
+
PB
)+(
OP
+
PC
)+(
OP
+
PD
)
=4
OP
+(
PA
+
PD
+
PB
+
PC
)
=4
OP
+(
PA
−
PA
+
PB
−
PB
)
( ∵ For a parallelogram P bisects the two diagonal.)
=4
OP
Hence, A is the correct option.
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