Practice Vector Addition, Subtraction, and Scalar Multiplication in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Vectors are added and subtracted component by component. Scalar multiplication multiplies each component of a vector by a number. If \mathbf{u} = \langle u_1, u_2 \rangle and \mathbf{v} = \langle v_1, v_2 \rangle, then \mathbf{u} + \mathbf{v} = \langle u_1 + v_1, u_2 + v_2 \rangle and k\mathbf{u} = \langle ku_1, ku_2 \rangle.

Vectors are arrows with direction and magnitude. Adding two vectors is like walking along the first arrow, then continuing along the second—you end up at the tip of the combined arrow (tip-to-tail method). Scalar multiplication stretches or shrinks the arrow: 2\mathbf{v} is twice as long in the same direction, while -\mathbf{v} points the opposite way.

Example 1

easy
If \mathbf{u} = \langle 3, -1 \rangle and \mathbf{v} = \langle 1, 4 \rangle, find 2\mathbf{u} - \mathbf{v}.

Example 2

medium
Find \mathbf{u} - \mathbf{v} where \mathbf{u} = \langle 2, 5, -1 \rangle and \mathbf{v} = \langle 4, -3, 2 \rangle.

Example 3

easy
Compute -3\langle 2, -4 \rangle.

Example 4

medium
Find the vector from point A(1, 3) to point B(4, -1).
← Back to Vector Addition, Subtraction, and Scalar Multiplication Worked Examples Formula Explained