Two-dimensional cross product
= Two-dimensional cross product
{title2=$u_xv_y-u_yv_x$}
For planar vectors $u=(u_x,u_y)$ and $v=(v_x,v_y)$, the scalar $u\times v=u_xv_y-u_yv_x$ is the <determinant> of their coordinate columns. It equals the perpendicular component of the three-dimensional <cross product> after embedding the plane in three dimensions. Its sign records orientation, and its absolute value is twice the <area> of the <triangle> spanned by $u,v$.