Wayground
Vector Operations - Printable Mathematics Worksheets - Wayground

Vector Operations

15 questions

11th - 11th Grade

Mathematics

Vector Operations is a free printable Grade 11 mathematics worksheet that develops fluency with component-form vector calculations. Across 15 items, students complete 14 multiple-choice questions and one fill-in-the-blank problem involving vector addition and subtraction, scalar multiplication, linear combinations, solving for unknown vector components, and converting vectors from points or diagrams into component form. The worksheet also asks students to calculate vector magnitude from initial and terminal coordinates, including rounding a result to the nearest tenth. This practice is useful for checking whether students can apply vector rules accurately while managing negative components and multi-step expressions. Teachers can use the questions for independent practice, a review assignment, or a quick assessment before more advanced vector work. The worksheet is available as a free printable PDF and includes a complete answer key for efficient checking.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Vector Operations

Total questions: 15

Name
Class
Date
1.

If c = <-5, 4> and d = <8, 0>, calculate 2c + d

a)

<-2, 8>

b)

<-2, 0>

c)

<6, 8>

d)

<6, 0>

2.
If y = <2, 0> and
z = <-1, -4>, find 3y - 2z.
a)
<5, -8>
b)
<4, 8>
c)
<8, 8>
d)
<-8, -8>
3.

Let u = <5, 2> and v = <1, -1>.


Find u + v.

a)

<4, -1>

b)

<6, 1>

c)

<3, 4>

d)

<1, 6>

4.
Find the components of a vector v such that 
v + 〈-6,4〉 = 〈10,-3〉
a)
〈4,1〉
b)
〈16,4〉
c)
〈16,-7〉
d)
none of these
5.

Given u = <3, 7> and v =<-5, 4>, find -u + v.

a)

<-8, -3>

b)

<8, 11>

c)

<-2, 11>

d)

<2, 3>

6.

If u = <-2, 0>, find 3u.

a)

<-6, 3>

b)

<-6, 0>

c)

<6, 0>

d)

<6, 3>

7.

Find the components of vector u, such that

<5, 8> - u = <-2, 10>

a)

<7, 2>

b)

<-7, 2>

c)

<-7, -2>

d)

<7, -2>

8.

If z = <-3, -3>, what is -4z?

a)

<12, 12>

b)

<12, -3>

c)

<-12, -12>

d)

<-12, 12>

9.

If y = <1, 1> and v = <6, 8>, what is 6y + 2v?

a)

<38, 50>

b)

<17, 30>

c)

<18, 22>

d)

16, 20>

10.

If u = <-3, 4>, v = <6, 8>, and y = <1, 1>, what is u + 3v + 2y?

a)

<16, 20>

b)

<17, 18>

c)

<23, 30>

d)

<17, 30>

11.

Which of the following is the component form for a vector with initial point (-1, 5) and terminal point (6, 8)?

a)

<-3, -7>

b)

<3, -7>

c)

<-3, 7>

d)

<7, 3>

12.

Write in component form.

a)

<-8, -2>

b)

<8, 2>

c)

<2, 8>

d)

<-2, -8>

13.
Find the magnitude of vector AB if the initial point is (-3, 1) and the terminal point is (3, 9).
a)
6
b)
8.2
c)
10
d)
10.4
14.

Find the magnitude of the vector with initial point (-8, 7) and terminal point (2, -5).

Round to the nearest tenth.

(a)  

15.

TU→+US→=\overrightarrow{TU}+\overrightarrow{US}=  

a)

TS→\overrightarrow{TS}  

b)

ST→\overrightarrow{ST}  

c)

VS→\overrightarrow{VS}  

d)

SV→\overrightarrow{SV}  

Answer Key

Vector Operations

Total questions: 15

1.
a)

<-2, 8>

2.
c) <8, 8>
3.
b)

<6, 1>

4.
c) 〈16,-7〉
5.
a)

<-8, -3>

6.
b)

<-6, 0>

7.
d)

<7, -2>

8.
a)

<12, 12>

9.
c)

<18, 22>

10.
d)

<17, 30>

11.
d)

<7, 3>

12.
b)

<8, 2>

13.
c) 10
14.
15.6
15.
a)

TS→\overrightarrow{TS}  

Browse by subjects

Browse by grades

Browse by format

FAQs

What does this Vector Operations worksheet help Grade 11 students practice?

This 15-item Grade 11 mathematics worksheet practices vector addition and subtraction, scalar multiplication, multi-term vector expressions, solving for unknown components, and writing vectors in component form. Its final problems require students to find magnitude from initial and terminal coordinates, including rounding one answer to the nearest tenth. The mix of 14 multiple-choice items and one fill-in-the-blank item checks both calculation accuracy and independent application.

How can I use this worksheet to teach vector operations in component form?

Introduce component-wise addition, subtraction, and scalar multiplication with a short worked example, then have students explain how each operation changes the horizontal and vertical components. Use the questions involving an unknown vector to connect symbolic equations with inverse operations, and use the initial-point and terminal-point items to show that component form is found by subtracting initial coordinates from terminal coordinates. Finish with the magnitude problems so students connect components to the distance formula.

What mistakes should I watch for when students complete this vector operations worksheet?

Watch for sign errors when students subtract vectors or multiply a vector by a negative scalar, especially in expressions such as -u + v and -4z. Students may also reverse terminal-minus-initial when finding component form from two points, or calculate magnitude without squaring both component differences. In the fill-in-the-blank magnitude item, check that students round the final value to the nearest tenth rather than rounding an intermediate step.

How do I assign and grade this Vector Operations worksheet?

On Wayground, you can assign Vector Operations as a printable PDF or as a digital quiz. The worksheet includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The PDF option also supports schools that want to reduce screen time while students practice component calculations and vector magnitude.

How can I differentiate this vector operations worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the vector equations, coordinate pairs, and answer choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language. These options create an alternate version of the same vector-operation and magnitude practice without changing the mathematical tasks.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion