ABCD-parallelogram, O- midpoint of intersection of diagonals AC and BD, M-midpoint BO.
| August 11, 2021 | education
ABCD-parallelogram, O- midpoint of intersection of diagonals AC and BD, M-midpoint BO. Express the CM vector in terms of AB and AD.
Vector | CM | = | СВ | + VM |.
Vector | СВ | = – | АD |, since the opposite sides of the parallelogram are equal, and the directions of the vectors are opposite.
Vector | ВD | = | DA | + | AB | = – | AD | + | AB |.
The diagonals of the parallelogram at the intersection point are divided in half, then BO = AD / 2, and BM = BO / 2 = BD / 4.
Then: | CM | = – | AD | + | ВD | / 4 = – | АD | + (| AD | + | AB |) / 4 = | AB | / 4 – 3 * | АD | / 4 = (| AB | – 3 * | AD |) / 4.
Answer: Vector | CM | is equal to (| AB | – 3 * | AD |) / 4.
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