In parallelogram ABCD, point M is taken on the diagonal AC so that AM: MC = 2: 3. Express the vector MA in terms of the vectors AB = a and AD = b.
Since, by condition, AM / MC = 2/3.
3 * AM = 2 * MC.
MC = 3 * AM / 2.
Since AM + CM = AC, then AC = AM + 3 * AM / 2 = 5 * AM / 2.
AM = 2 * AC / 5.
Vector | AC | = | AB | + | AD | = | a | + | b |.
| AM | = 2 * (a + b) / 5.
Then | MA | = – | AM | = -2 * (a + b) / 5.
Answer: The MA vector is -2 * (a + b) / 5.
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