In the parallelogram ABCD on the side AD, the point M is taken so that AM: MD = 3: 4
| April 29, 2021 | education
In the parallelogram ABCD on the side AD, the point M is taken so that AM: MD = 3: 4 express the vector CM through the vectors CB = a and CD = b.
Since AM / MD = 3/4, then 3 * MD = 4 * AM.
AM = 3 * MD / 4.
DA = AM + MD = 3 * MD / 4 + MD = 7 * MD / 4.
MD = 4 * DA / 7.
Since the opposite sides of the parallelogram are equal, then DA = CB = a, then MD = 4 * a / 7.
The CM vector is equal to the sum of the CD and DM vectors. | CM | = | CD | + | DM | = b + 4 * a / 7.
Answer: The length of the CM vector is b + 4 * a / 7.
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