In the parallelogram ABCD, point M lies on the side BC, BM: MC = 3: 2. Express the vector MA

univerkov | August 11, 2021 | education

In the parallelogram ABCD, point M lies on the side BC, BM: MC = 3: 2. Express the vector MA in terms of vectors AB and AD.

Vector | ↑ MA | = | ↑ MB | + | ↑ BA |.

Since ABCD is a parallelogram, its opposite sides are equal, and then the vector ↑ СВ = ↑ DA = – ↑ AD.

By condition, ВM / MС = 3/2, then 2 * ВM = 3 * MS.

MС = BM * 2/3.

BC = ВM + MС = ВM + ВM * 2/3 = 5 * ВM / 3.

ВM = 3 * BC / 5.

Then the vector | ↑ ВM | = -3 * | ↑ AD | / five.

Vector | ↑ ВA | = – | ↑ AB |.

Then | ↑ MA | = -3 * | ↑ AD | / 5 – | ↑ AB | = – (3 * | ↑ АD | / 5 + | ↑ AB |).

Answer: | ↑ MA | = – (3 * | ↑ АD | / 5 + | ↑ AB |).

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