Vector Geometry Flashcards

A vector is written as a column vector (e.g., \( \begin{pmatrix} a \\ b \end{pmatrix} \)) or using bold letters (e.g., \( \mathbf{a} \)).

A vector written as \( \begin{pmatrix} a \\ b \end{pmatrix} \), where \(a\) is the horizontal component and \(b\) is the vertical component.

The length of a vector, calculated as \( \sqrt{a^2 + b^2} \) for a vector \( \begin{pmatrix} a \\ b \end{pmatrix} \).

To add two vectors, add their corresponding components: \( \begin{pmatrix} a \\ b \end{pmatrix} + \begin{pmatrix} c \\ d \end{pmatrix} = \begin{pmatrix} a+c \\ b+d \end{pmatrix} \).

To subtract two vectors, subtract their corresponding components: \( \begin{pmatrix} a \\ b \end{pmatrix} - \begin{pmatrix} c \\ d \end{pmatrix} = \begin{pmatrix} a-c \\ b-d \end{pmatrix} \).

To multiply a vector by a scalar \(k\), multiply each component by \(k\): \( k \begin{pmatrix} a \\ b \end{pmatrix} = \begin{pmatrix} ka \\ kb \end{pmatrix} \).

Two vectors are parallel if one is a scalar multiple of the other (e.g., \( \mathbf{a} = k \mathbf{b} \)).

A vector that represents the position of a point relative to the origin, written as \( \begin{pmatrix} x \\ y \end{pmatrix} \).

The vector obtained by adding two or more vectors together.

Operations such as addition, subtraction, and scalar multiplication performed on vectors.