Vectors: FAQ

A vector is a mathematical object that has both a magnitude (length) and a direction. Vectors can be used to represent physical quantities such as velocity, force, and acceleration.

Vector components are the horizontal and vertical parts of a vector. They can be found using trigonometric functions and the magnitude and direction of the vector.

There are a few different ways to add and subtract vectors. One way is to use vector components: you add or subtract the corresponding horizontal and vertical components to find the components of the resulting vector. Another way is to use vector magnitude and direction: you convert both vectors into this form, add or subtract the magnitudes, and use trigonometry to find the direction of the resulting vector.

Multiplying a vector by a scalar (a number) changes its magnitude but not its direction. To multiply a vector by a scalar, you multiply each of its components by the scalar. For example, if $\overrightarrow{v}=(3,4)$‍ and $k=2$‍, then $k\overrightarrow{v}=(6,8)$‍.

Vectors are used in a wide variety of fields. In physics, vectors are used to describe motion (velocity, acceleration, force), while in engineering they are used to understand and design structures. Vectors are also used in computer graphics, where they are used to create and transform shapes.