Representing Vectors in WeBWorK- A Tutorial

Representing Vectors in WeBWorK: What Actually Works

WeBWorK is particular about how you enter vectors. One wrong bracket or missing comma and your answer gets marked wrong even when your math is correct. This tutorial cuts through the confusion and shows you exactly how to represent vectors in WeBWorK problems.

Basic Vector Syntax

Most WeBWorK problems use one of three vector representations: angle bracket notation, column vectors, or coordinate lists. The method your problem expects depends on how the answer checker is configured.

Angle Bracket Notation

The most common format is angle brackets with comma separation:

<1, 2, 3>

This represents the vector (1, 2, 3) in 3D space. You can also use this for 2D vectors:

<4, -1>

Spaces after commas are optional but improve readability.

Column Vector Format

Some problems expect vectors written vertically:

<1, 2, 3> looks identical in input but may render differently depending on the problem's answer checker. The key is matching what the problem explicitly asks for.

List Format (Caution Required)

Never enter vectors as plain lists like (1, 2, 3) unless the problem specifically allows it. WeBWorK interprets parentheses as grouping symbols, not vector notation. You'll get errors or incorrect grading.

Vector Operations in WeBWorK

Once you have vector syntax down, you need to know how to perform operations correctly.

Addition and Subtraction

Enter operations using angle brackets:

<1, 2, 3> + <4, 5, 6>

The result should be <5, 7, 9>. WeBWorK evaluates these before checking your answer.

Scalar Multiplication

Multiply a vector by a scalar:

3*<1, 2, 3>

This gives <3, 6, 9>. You can also write it as <3, 6, 9> directly.

Dot Product

For dot products, you typically need to use the mod() function or compute manually:

<1, 2, 3> · <4, 5, 6> = 1*4 + 2*5 + 3*6 = 32

Enter the scalar result as your answer, not the vector.

Cross Product

Enter cross products using $v x $w syntax in PG problems. For student answers, compute the result first:

<1, 0, 0> x <0, 1, 0> = <0, 0, 1>

Common Mistakes That Break Your Answers

These errors account for most incorrect submissions:

Wrong brackets: Using parentheses () instead of angle brackets <>
Missing commas: Writing <1 2 3> instead of <1, 2, 3>
Extra spaces in wrong places: Some checkers are sensitive to formatting
Forgetting the magnitude notation: When asked for magnitude, enter a scalar, not a vector
Using coordinate notation: Writing (x, y, z) instead of <x, y, z>

Vector Functions You Need to Know

WeBWorK provides built-in functions for common vector operations:

mod(v) or norm(v) — returns the magnitude of vector v
Unit(v) — returns the unit vector in the direction of v
dot(u, v) — computes the dot product of u and v
cross(u, v) — computes the cross product of u and v

How to Enter Answers: Getting Started

Follow these steps when you encounter a vector problem:

Read the instructions carefully. The problem tells you exactly what format to use. If it says "enter as <a,b,c>", do exactly that.
Identify the dimension. 2D vectors have 2 components, 3D have 3. Mismatching dimensions is an automatic wrong answer.
Check for signs. Negative numbers are entered with the minus sign, like <3, -2, 0>.
Use exact values. WeBWorK distinguishes between 1/2 and 0.5. Enter fractions as 1/2, not 0.5, unless specified otherwise.
Preview before submitting. Most WeBWorK interfaces have a preview button. Use it.

Comparing Vector Input Methods

Usually causes syntax errors

Format	Example	When to Use	Common Errors
Angle Brackets	`<1, 2, 3>`	Standard vector input in most problems	Using parentheses instead
Column Vector	`<1, 2, 3>`	Matrix or linear algebra problems	Forgetting to match dimensions
List Format	`(1, 2, 3)`	Only when explicitly allowed
Polar Coordinates	`<r, theta>`	Physics or engineering problems	Using degrees instead of radians

Context-Specific Tips

Physics Problems

Physics problems often use unit vector notation like i, j, k or <1, 0, 0>. If the problem asks for a vector in component form, use angle brackets. If it asks for magnitude and direction, enter two separate answers if prompted.

Linear Algebra Problems

Linear algebra often involves vectors in R^n. The syntax is the same, but the context changes what operations are valid. A vector in R^4 needs four components, not three.

Calculus Problems

For tangent vectors or normal vectors to curves and surfaces, your answer must match the direction. A vector and its negative are both valid if the problem allows scalar multiples. Check if your problem has "accept any vector parallel to..." enabled.

When Your Answer Is Marked Wrong Despite Being Correct

This happens. Here's how to debug:

Check the formatting. Is it <1,2,3> or <1, 2, 3>? Try both.
Verify the dimension. Did you enter a 3D vector when the problem wanted 2D?
Check for equivalent answers. <2, 4, 6> and <1, 2, 3> point in the same direction but have different magnitudes.
Look at the error message. WeBWorK sometimes tells you exactly what's wrong.
Ask your instructor. If everything looks correct and it still fails, there may be a problem with the answer checker configuration.

The Bottom Line

Representing vectors in WeBWorK comes down to three rules: use angle brackets, separate components with commas, and match the dimension the problem expects. Once you internalize these, vector problems become straightforward. The confusion mostly comes from not reading what format the specific problem requires.