Given v = (2, -3, 4), find 3v.

Step 1: Recall scalar multiplication.

To multiply a vector by a scalar, multiply every component of the vector by that scalar.

The vector is:
v = (2, -3, 4)

The scalar is 3.

Step 2: Multiply each component by 3.

3(2) = 6
3(-3) = -9
3(4) = 12

Step 3: Write the resulting vector.

3v = (6, -9, 12)

Therefore, 3v = (6, -9, 12).