What formula is the multiplication of vector AB and vector AC, and what formula is the addition

What formula is the multiplication of vector AB and vector AC, and what formula is the addition

If vector AB = (a, b), vector AC = (C, d)
Then the vector AB * vector AC = a * C + b * D
Vector AB + vector AC = (a + C, B + D)
Where a = XB Xa, B = Yb ya, C = XC Xa, d = YC ya