We can use the fact that the sum of two vectors is equal to the third vector to find the values of x, y, and z.
AB + BC = AC
(1, y, -2) + (2x, -3, z) = (1, 4, x+y)
Breaking down each component, we get:
1 + 2x = 1 → 2x = 0 → x = 0
y - 3 = 4 → y = 7
-2 + z = x + y → z = x + y + 2
Therefore, the values of x, y, and z are:
x = 0
y = 7
z = x + y + 2 = 9