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Vectors (Metric)

Class Details

Tom Baker

Learn, or revise, vector quantities, the scalar product and the vector equations of lines and planes.

Introduction to Vectors

Vectors, and their magnitude and direction.

The relation \(|a\,{\bf i}+b\,{\bf j}+c\,{\bf k}|=\sqrt{a^2+b^2+c^2}\).

Lesson Not yet graded

"Pure direction": the vector of length 1 parallel to a given vector.

Lesson Not yet graded

Vector Equation of a Line

The equation of a line in 3D.

Line through a given point in a given direction; line through two points.

Lesson Not yet graded

For a 3D line, the equations linking \(x\), \(y\) and \(z\).

Lesson

Are these lines parallel, do they meet at a point or do they miss one another entirely?

Lesson Not yet graded

The Scalar Product

The scalar product of two vectors, and using it to calculate angles.

The scalar product \({\bf a}\cdot{\bf b}=a\,b\,\cos\theta\), and using it to calculate \(\theta\).

Lesson Not yet graded

Closest distance of approach between a given line and a given point.

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Vector Equation of a Plane

The equation of a plane in 3D.

The equation of a plane through a given point, perpendicular to a given vector.

Lesson Not yet graded

Distance of a plane from the origin, and distance between two parallel planes.

Lesson Not yet graded

The scalar product \({\bf a}\times{\bf b}=a\,b\,\sin\theta\,{\bf n}\), and using it to calculate a vector perpendicular to two given vectors.

Lesson Not yet graded

The triple product \({\bf a}\cdot({\bf b}\times{\bf c})\) and its applications.

Lesson
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