91Ó°ÊÓ

To draw the given vectors, plot them on a 2D plane where the x-coordinate is the horizontal axis and the y-coordinate is the vertical axis. Begin by drawing an arrow representing \(\mathbf{u}=(2,1)\), starting from the origin (0,0) and ending at the point (2,1). Next, draw an arrow representing \(\mathbf{v}=(3,1)\), starting from the origin (0,0) and ending at the point (3,1). Now to illustrate the subtraction \(\mathbf{u}-\mathbf{v}\), move the vector \(\mathbf{v}\), so its tail coincides with the head of the vector \(\mathbf{u}\). Draw a new arrow starting from the point at the head of \(\mathbf{u}\) and ending at the point at the head of the moved \(\mathbf{v}\). This new arrow represents the vector \(\mathbf{u}-\mathbf{v}\).

To compute the difference of the two vectors, subtract the corresponding coordinates of \(\mathbf{v}\) from the coordinates of \(\mathbf{u}\). This can be done using the following formula: \(\mathbf{u}-\mathbf{v} = (u_x-v_x, u_y-v_y)\) Substitute the coordinates of \(\mathbf{u}\) and \(\mathbf{v}\) into the equation: \((2,1)-(3,1) = (2-3, 1-1)\) Subtract the coordinate values: \((-1,0)\) The vector difference \(\mathbf{u}-\mathbf{v}\) is \((-1,0)\).