Resources tagged “vectors”

12 resources.

Operations on Vectors

The negative of a vector, the scalar triple product identity, and using the dot product on unit vectors, with worked examples.

Finding a Unit Vector

How to find the unit vector in a given direction, between two points, or scaled to a target magnitude, with worked examples.

Projection of a Vector

What the projection of a vector onto a directed line means, including what happens at special angles, with a worked example.

Finding the Position Vector of a Point

The section formula for a point dividing a segment internally or externally, and finding a midpoint, with worked examples.

Finding Direction Cosines

What direction cosines are and how to find them for a coordinate axis, a line through two points, or a line at given angles.

Finding the Equation of a Line

Writing a line's equation in vector and Cartesian form, given two points or a point and a parallel vector, with worked examples.

Finding the Equation of a Plane

The equation of a coordinate plane, and finding a plane through the intersection of two others and a given point, with a worked example.

Finding the Intercepts of a Plane

How to read a plane's intercepts on each axis straight from its equation, with a worked example.

Angle Between a Line and a Plane

How to find the angle between a line and a plane using their direction vector and normal vector, with a worked example.

Shortest Distance Between Two Lines

The formula for the shortest distance between two skew lines in vector form, with two fully worked examples.

Area of a Triangle and Parallelogram Using Vectors

Using the cross product to find the area of a triangle or parallelogram from vertex or side vectors, with worked examples.

Vector Calculus: Gradient, Divergence, and Curl

The gradient, divergence, and curl operators explained, with worked examples computing each directly from a scalar and a vector field.