ABCD – parallelogram, point m – midpoint of CD. Expand BM into DA and DC vectors.

univerkov | January 28, 2021 | education

Vector | ВM | is the sum of vectors | BC | and | CM |.

Vector | Sun | = – | AD |, since their values are equal as opposite sides of the parallelogram, and the directions are opposite.

Since point M is the middle of the СD, then the segment CM = MD = AD / 2.

Then the vector | CM | = – | SD | / 2.

Vector | ВM | = | Sun | + | CM | = – | AD | + (- | СD | / 2) = – (| AD | + | СD | / 2).

Answer: | ВM | = – (| AD | + | СD | / 2).

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