The median of a triangle is a vector from a vertex to the midpoint of the opposite side.
Show the sum of the medians of a triangle = 0.
Answer: The median of side AB is the vector from vertex C to the midpoint of AB. Label
this midpoint as P. As usual we write P for the origin vector
−−→
OP.
−−→
CP =
1
2
(A + B)
1
The midpoint P = ⇒ (B + A) − C.
2
Likewise:
−−→
BQ = (A + C) − B and
−−→
AR =
1
2
1
2
(B + C)

Question

The median of a triangle is a vector from a vertex to the midpoint of the opposite side.
Show the sum of the medians of a triangle = 0.
Answer: The median of side AB is the vector from vertex C to the midpoint of AB. Label
this midpoint as P. As usual we write P for the origin vector
−−→
OP.
−−→
CP =
1
2
(A + B)
1
The midpoint P = ⇒ (B + A) − C.
2
Likewise:
−−→
BQ = (A + C) − B and
−−→
AR =
1
2
1
2
(B + C)

anonymous · Answer

Why is it -c and not +c?

anonymous · Answer

Geometrically I do not see what is happening when we subtract that

anonymous · Answer

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_we_4_comb.pdf