I have the points O,A,B and C.Relative to O, the position vectors of A, B...

Rishi Hale

Rishi Hale

Answered

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 1 2 O B = O A + 1 2 A C ?
Are there other ways using vectors?

Answer & Explanation

salumeqi

salumeqi

Expert

2022-07-24Added 15 answers

Yes, your method is correct.
You may also show that
O A = C B
and
O C = A B
which make the quadrilateral OABC into a parallelogram where the diagonals bisect each other.

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