In parallelogram ABCD, point M is taken on the diagonal AC so that AM: MC = 2: 3. Express the vector MA

univerkov | March 31, 2021 | education

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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