Practice Vector Addition in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Vector addition combines vectors component-wise or head-to-tail to produce a resultant vector.

Walk one arrow, then another; the single shortcut arrow is their sum.

Showing a random 20 of 50 problems.

Example 1

medium
The resultant of a⃗+b⃗ is the diagonal of what shape formed by a⃗ and b⃗?

Example 2

medium
If a⃗=⟨1,2⟩ and a⃗+b⃗=⟨1,2⟩, what is b⃗?

Example 3

easy
Add ⟨−4,7⟩+⟨9,−2⟩.

Example 4

challenge
Three vectors sum to zero: ⟨2,3⟩+⟨−5,1⟩+c⃗=0⃗. Find c⃗.

Example 5

challenge
Let a⃗=⟨1,2⟩ and b⃗=⟨3,−1⟩. Find scalars s,t such that sa⃗+tb⃗=⟨11,1⟩.

Example 6

easy
Add ⟨0,5⟩+⟨4,0⟩.

Example 7

easy
Add ⟨2,3⟩+⟨2,3⟩.

Example 8

easy
Add ⟨5,−3⟩+⟨−5,3⟩.

Example 9

easy
Fill in the blank: a⃗+0⃗= ____.

Example 10

medium
Find the resultant of ⟨6,−2⟩, ⟨−3,5⟩, ⟨4,1⟩, and ⟨−2,−4⟩.

Example 11

medium
A person walks ⟨3,0⟩ then ⟨0,4⟩. What single displacement vector results?

Example 12

hard
Find a vector c⃗ such that ⟨2,−3,5⟩+⟨−1,4,−2⟩+c⃗=⟨0,0,0⟩.

Example 13

challenge
If u⃗+v⃗=⟨5,7⟩ and u⃗−v⃗=⟨1,3⟩, find u⃗.

Example 14

easy
What is the resultant of ⟨3,0⟩+⟨0,4⟩?

Example 15

easy
Is ⟨1,2⟩+⟨3,4,5⟩ defined?

Example 16

medium
If a⃗+b⃗=⟨10,6⟩ and a⃗=⟨4,9⟩, find b⃗.

Example 17

easy
Add ⟨−2,5⟩+⟨6,−1⟩.

Example 18

easy
True or false: a⃗+b⃗=b⃗+a⃗ for all vectors of the same dimension.

Example 19

medium
Add ⟨4,−2⟩+⟨−1,6⟩+⟨2,1⟩.

Example 20

medium
Find ⟨2,−1⟩+⟨5,3⟩+⟨−1,2⟩.
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