Vectors

2D and 3D vector representation, position and displacement vectors, vector addition and subtraction, scalar multiples and unit vectors, magnitudes and parallel/perpendicular vectors, scalar and vector products, angles and areas, and vector equations of lines and motion models.

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Vector arithmetic & geometry

3D and 2D vector notation with base vectors and position vectors, including zero and negative vectors, scalar multiples, unit vectors, vector magnitude, addition and subtraction by components or triangle law, displacement vectors, and parallel vectors.

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Scalar product

The scalar (aka dot) product, and its connection to angles between vectors.

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Vector Product

The vector (aka cross) product u×v and its connection to areas in 3D space.

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Equations of a vector line

Equations of a vector line in 3D using a point and direction vector, written in vector form r=a+λb or parametric form x=x0+λl, y=y0+λm, z=z0+λn, with applications to motion and angles between lines.

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Vectors

2D and 3D vector representation, position and displacement vectors, vector addition and subtraction, scalar multiples and unit vectors, magnitudes and parallel/perpendicular vectors, scalar and vector products, angles and areas, and vector equations of lines and motion models.

Sign up to view your learning progress

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Learning path

Follow the recommended order, or open any concept.

Start Here

Vector arithmetic & geometry

3D and 2D vector notation with base vectors and position vectors, including zero and negative vectors, scalar multiples, unit vectors, vector magnitude, addition and subtraction by components or triangle law, displacement vectors, and parallel vectors.

0/0 key exercises

Scalar product

The scalar (aka dot) product, and its connection to angles between vectors.

0/0 key exercises

Vector Product

The vector (aka cross) product u×v and its connection to areas in 3D space.

0/0 key exercises

Equations of a vector line

Equations of a vector line in 3D using a point and direction vector, written in vector form r=a+λb or parametric form x=x0+λl, y=y0+λm, z=z0+λn, with applications to motion and angles between lines.