Vectors

Vectors are quantities that have both magnitude (size) and direction. This branch of maths is fundamental to physics and engineering to represent physical quantities that have a direction. Use these resources to increase your understanding of vectors.

1. Getting started
   • Introduction to vectors
     Use this resource to gain a basic understanding of vectors, including different types of vectors, how to apply operations to them, and how to calculate the magnitude of a vector.
   • Resolution of vectors
     Use this resource to learn how to find the resolution of vectors—that is, separate them into their components.
   • Scalar or dot product
     Use this resource to learn how to multiply two vectors using the scalar or dot product.
   • Projection of vectors
     Use this resource to learn how to project a vector along the line of another vector.
2. Next steps
   • Vector or cross product
     Use this resource to learn how to multiply two vectors using the vector or cross product.
   • Equation of a line in 3D
     Use this resource to learn how to define an equation for a line that represents a vector in three-dimensional space.
   • Intersecting lines in 3D
     Use this resource to learn how to find the point of intersection between two vectors defined by lines in three-dimensional space.
3. Dive deeper
   • Equation of a plane in 3D
     Use this resource to learn how to define an equation that represents a two-dimensional vector plane within a three-dimensional space.
   • Intersecting planes in 3D
     Use this resource to learn how to determine the angle between two intersecting planes and the equation of the line of intersection.
   • Distance from a point to a plane
     Use this resource to learn how to find the distance between a point and a plane using vectors.
   • Directional derivatives
     Use this resource to learn how to calculate directional derivatives.