Component Vector Operations

You can add vectors if you split into components then perform the operation for each components.

Vector Addition

$\overrightarrow{[x_1,y_1]}+\overrightarrow{[x_2,y_2]}=\overrightarrow{[x_1+x_2,y_1+y_2]}$

Example

$\overrightarrow{[2,3]}+\overrightarrow{[6,2]}=\overrightarrow{[8,5]}$

Vector Subtraction

$\overrightarrow{[x_1,y_1]}-\overrightarrow{[x_2,y_2]}=\overrightarrow{[x_1-x_2,y_1-y_2]}$

Example

$\overrightarrow{[27,3]}-\overrightarrow{[6,2]}=\overrightarrow{[21,1]}$

Vector Scalar Multiplication

$m\overrightarrow{[x,y]}=\overrightarrow{[mx,my]}$