Vector Addition Flashcards

A quantity with both magnitude and direction, represented by an arrow.

A vector written in the form \( \begin{pmatrix} x \\ y \end{pmatrix} \), where \(x\) is the horizontal component and \(y\) is the vertical component.

The process of adding two vectors by adding their corresponding components.

Add the horizontal components together and the vertical components together: \( \begin{pmatrix} a \\ b \end{pmatrix} + \begin{pmatrix} c \\ d \end{pmatrix} = \begin{pmatrix} a+c \\ b+d \end{pmatrix} \).

The vector obtained after adding two or more vectors.

A vector with both components equal to zero: \( \begin{pmatrix} 0 \\ 0 \end{pmatrix} \).

Subtract the corresponding components: \( \begin{pmatrix} a \\ b \end{pmatrix} - \begin{pmatrix} c \\ d \end{pmatrix} = \begin{pmatrix} a-c \\ b-d \end{pmatrix} \).

Multiply each component of the vector by the scalar: \( k \begin{pmatrix} a \\ b \end{pmatrix} = \begin{pmatrix} ka \\ kb \end{pmatrix} \).

Place the tail of the second vector at the head of the first vector. The resultant vector is drawn from the tail of the first vector to the head of the second vector.

Vector addition is commutative: \( \mathbf{a} + \mathbf{b} = \mathbf{b} + \mathbf{a} \).