find the vector from origin to the midpoint of the vector p1p2 joining the points
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Step-by-step explanation:
Let the midpoint of PQ be R
Position vector of P=(2−0)
i
^
+(3−0)
j
^
+(4−0)
k
^
OP
=2
i
^
+3
j
^
+4
k
^
Position vector of Q=(4−0)
i
^
+(1−0)
j
^
+(−2−0)
k
^
OQ
=4
i
^
+
j
^
−2
k
^
Now,
Position vector of R=
2
OQ
+
OP
OR
=
2
(4
i
^
+
j
^
−2
k
^
)+(2
i
^
+3
j
^
+4
k
^
)
OR
=
2
(4+2)
i
^
+(1+3)
j
^
+(−2+4)
k
^
OR
=
2
6
i
^
+4
j
^
+2
k
^
OR
=
2
2(3
i
^
+2
j
^
+
k
^
)
OR
=3
i
^
+2
j
^
+
k
^
Therefore, position vector of midpoint of PQ is 3
i
^
+2
j
^
+
k
^
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