Position Vectors (Edexcel A-Level Mathematics): Flashcards

It represents a point's position relative to a fixed origin.

As $r = (x, y)$ where $(x, y)$ are the point's coordinates.

As $r = (x, y, z)$ where $(x, y, z)$ are the coordinates.

$|r| = \sqrt{x^2 + y^2}$ for a 2D position vector.

$|r| = \sqrt{x^2 + y^2 + z^2}$ for a 3D vector.

Vectors are collinear if they lie on the same line.

Displacement $AB = b - a$ for position vectors $a$ and $b$.

By normalizing the vector or using direction cosines.

Change in position vector over time gives the velocity.

Check if the area of triangle ABC is zero.