Vectors — Chapter Summary

A scalar is a quantity

A scalar is a quantity that has only magnitude, such as length, mass, or temperature. A vector has both magnitude and direction, such as displacement,

A vector is denoted by

A vector is denoted by a directed line segment like \(\overrightarrow{AB}\), where A is the initial point and B is the terminal point. Important types

Vectors are added using the triangle

Vectors are added using the triangle law or parallelogram law. For two vectors \(\vec{a}\) and \(\vec{b}\), the sum \(\vec{a} + \vec{b}\) is the vecto

Multiplying a vector \(\vec{a}\) by

Multiplying a vector \(\vec{a}\) by a scalar \(k\) results in a vector \(k\vec{a}\) whose magnitude is \(|k|\) times that of \(\vec{a}\). The directio

The position vector of a point

The position vector of a point P relative to origin O is \(\overrightarrow{OP}\). If a point divides the line segment joining points with position vec