Stage 27 · Plane Vectors

27.4.5 Finding Length and Angle with the Dot Product

27.4 The Dot Product: Angles and Perpendicularity

Point 5 of 7

27.4.5 Finding Length and Angle with the Dot Product

Core idea

Dot a vector with itself and take the square root to get its length, |a|=√(a·a); then rearrange the cosθ formula to recover the angle.

Module goal. Introduce the operation that multiplies two vectors into a number, capturing the angle between them, projection, and when they're perpendicular.
eastmath.com · 27.4 The Dot Product: Angles and Perpendicularity · 27.4.5 Finding Length and Angle with the Dot Product