2D vector calculator

Operations on vectors in the plane. Addition and subtraction are done component by component: $\vec{a}+\vec{b}=[a_x+b_x,\ a_y+b_y]$. The magnitude (length) of a vector is:

$|\vec{a}|=\sqrt{a_x^2+a_y^2}$

The dot product $\vec{a}\cdot\vec{b}=a_x b_x+a_y b_y$ lets you find the angle between the vectors:

$\cos\theta=\frac{\vec{a}\cdot\vec{b}}{|\vec{a}|\,|\vec{b}|}$

The calculator draws both vectors and their resultant. When the dot product is 0, the vectors are perpendicular.