In the parallelogram abcd, the point f lies on the diagonal AC Af: fc = 4: 3, express the vector

In the parallelogram abcd, the point f lies on the diagonal AC Af: fc = 4: 3, express the vector bf through the vectors ba = a and bc = b

Vector ВF is equal to the sum of vectors ВС and СF.

By condition, the vector ВС = b.

We define the vector СF, for which we first find the vector АС. Vector AC = AB + BC = -BA + BC = -a + b = b – a.

CA = a – b.

Since, by condition, AF / FC = 4/3, then СF = 3 * CA / 7 = 3 * (a– b) / 7.

Then the vector BF = b + 3 * (a – b) / 7 = (3 * a / 7) + (4 * b / 7).

Answer: Vector BF = (3 * a / 7) + (4 * b / 7).