Rishi Hale

2022-07-23

I have the points O,A,B and C.
Relative to O, the position vectors of A, B and C are (1,4,2), (3,3,3), (2,−1,1)
Want to show that the lines OB and AC bisect each other.
Is it sufficient to show that $\frac{1}{2}\stackrel{\to }{OB}=\stackrel{\to }{OA}+\frac{1}{2}\stackrel{\to }{AC}$?
Are there other ways using vectors?

salumeqi

Expert

You may also show that
$\stackrel{\to }{OA}=\stackrel{\to }{CB}$
and
$\stackrel{\to }{OC}=\stackrel{\to }{AB}$
which make the quadrilateral OABC into a parallelogram where the diagonals bisect each other.

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