First you'll learn to understand vectors as a shift in space, before learning to and and subtract them, work out their magnitude and direction, and break down vectors into their components.

Learn how vectors can represent shifts on the coordinate plane.

Vectors

/courses/vectors/vectors/vector-addition/

Vector Addition

/courses/vectors/vectors/drawing-vector-sums/

Drawing Vectors

/courses/vectors/vectors/vector-addition-component-wise/

Component-Wise Addition

/courses/vectors/vectors/practice/vectors-level-1-review-1/

Level Review

Vector Subtraction

/courses/vectors/vector-subtraction/opposite-vectors/

Opposite Vectors

/courses/vectors/vector-subtraction/vector-subtraction/

/courses/vectors/vector-subtraction/drawing-vector-differences/

Drawing Differences

/courses/vectors/vector-subtraction/vector-differences/

Vector Differences

/courses/vectors/vector-subtraction/practice/vectors-level-2-review-1/

Scale vectors and add them together to form linear combinations.

Linearly interpolate between two vectors.

Linear Combinations

/courses/vectors/linear-combinations/scalar-multiplication/

Scalar Multiplication

/courses/vectors/linear-combinations/negative-scalar-mult/

Reversing Direction

/courses/vectors/linear-combinations/linear-combinations/

/courses/vectors/linear-combinations/solving-linear-combinations/

Solving Linear Combinations

/courses/vectors/linear-combinations/drawing-linear-combinations/

Drawing Linear Combinations

/courses/vectors/linear-combinations/linear-interpolation/

Linear Interpolation

/courses/vectors/linear-combinations/practice/vectors-level-3-review-1/

Describe a vector in terms of its magnitude and polar angle.

Magnitude and Direction

/courses/vectors/magnitude-and-directions/magnitude-and-direction/

/courses/vectors/magnitude-and-directions/plotting-from-magnitude-direction/

Drawing from Polar Form

/courses/vectors/magnitude-and-directions/inverse-tangent/

Polar Angles

/courses/vectors/magnitude-and-directions/finding-the-angle/

Finding the Polar Angle

/courses/vectors/magnitude-and-directions/computing-angles/

Computing from Components

/courses/vectors/magnitude-and-directions/practice/vectors-level-4-review-1/

Compute the components of a vector from magnitude and polar angle.

Add vectors by first finding their components.

Components from Angles

/courses/vectors/components-from-angles/vector-components-from-d-and-m/

Vector Components

/courses/vectors/components-from-angles/equivalent-expressions-2/

Non-Polar Angles

/courses/vectors/components-from-angles/combining-vectors-from-d-and-m/

Combining Vectors

/courses/vectors/components-from-angles/practice/vectors-level-5-review-1/

Master vector operations from addition and subtraction to linear combinations and polar form.

Vectors

Level 1Vectors

Level 2Vector Subtraction

Level 3Linear Combinations

Level 4Magnitude and Direction

Level 5Components from Angles

Course description

Topics covered

Prerequisites and next steps

Vectors

.css-1c3z9fl{color:var(--bits-colors-gray-700);text-transform:uppercase;font-size:var(--bits-fontSizes-xs);font-weight:var(--bits-fontWeights-bold);line-height:1.1;letter-spacing:0.48px;}Level 2Vector Subtraction

Level 3Linear Combinations

Level 4Magnitude and Direction

Level 5Components from Angles

Course description

Topics covered

Prerequisites and next steps

Level 2Vector Subtraction