Find the dot product of u = (2, -1, 3) and v = (4, 5, -2).

Step 1: Recall the dot product formula.

For vectors u = (u1, u2, u3) and v = (v1, v2, v3):

u · v = u1v1 + u2v2 + u3v3

Step 2: Substitute the components.

u · v = (2)(4) + (-1)(5) + (3)(-2)

Step 3: Multiply each pair of corresponding components.

(2)(4) = 8
(-1)(5) = -5
(3)(-2) = -6

Step 4: Add the products.

u · v = 8 - 5 - 6
u · v = -3

Therefore, the dot product is -3.