Let's assume vector a = (a1, a2) and vector b = (b1, b2).

Given:

vector a + vector b = (5, 6) -- (Equation 1)

vector a - vector b = (3, 2) -- (Equation 2)

Adding Equation 1 and Equation 2, we get:

2 * vector a = (5, 6) + (3, 2)

2 * vector a = (8, 8)

vector a = (4, 4)

Subtracting Equation 2 from Equation 1, we get:

2 * vector b = (5, 6) - (3, 2)

2 * vector b = (2, 4)

vector b = (1, 2)

Therefore, vector a = (4, 4) and vector b = (1, 2).