KMNP-parallelogram Express the vectors MA and AB in terms of vectors m = KM

univerkov | February 1, 2021 | education

KMNP-parallelogram Express the vectors MA and AB in terms of vectors m = KM and n = KP, where point A is on the segment PN such that PA: AN = 2: 1, B is the midpoint of the segment MN.

By condition, RA / AH = 2/1, then RA = 2 * AN.

AN + RA = PH = KM.

AH + 2 * AH = KM.

3 * AH = KM.

AH = KM / 3.

The HA vector is opposite to the KM vector and is equal to its third part. Vector HA = -m / 3.

The vector MH = n, then the vector MA = MH + HA = n – (m / 3).

Point B, by condition, is the middle of MH, then Vector BH = MH / 2 = n / 2.

Then the vector НВ = -ВН = -n / 2.

Vector AH = m / 3.

Vector AB = AH + HB = (m / 3) – (n / 2).

Answer: Vector MA = n – (m / 3), vector AB = (m / 3) – (n / 2).

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