Vector Addition

Vector \(\vec{r_1}\)
\(x_1 =\)
\(y_1 =\)
\(r_1 =\)
\(\theta_1 =\) °
Vector \(\vec{r_2}\)
\(x_2 =\)
\(y_2 =\)
\(r_2 =\)
\(\theta_2 =\) °
Vector Sum, \(\vec{r_1}+\vec{r_2}\)
\(x = \)
\(y = \)
\(r = \)
\(\theta = \) °

The above grid represents a two-timensional \( xy \)-space where we can place two vectors, and perform their vector addition. As you click-and/or-drag to place the first vector, its components, magnitude and direction are displayed (the direction is given in degrees, positive for vectors in the first and second quadrant and negative for vectors in the third and fourth quadrant). As you release, the vector is created (in blue), and you can now click-and/or-drag to place the second vector (in red). Both vectors must be placed inside the central part, the [-10,10] range along both axes, otherwise their sum may end up being too big to fit inside the [-20,20] range of the grid. A "Clear" button allows you to remove the last vector you added; an "All Clear" allows you to start all over again.

Once you have two vectors, clicking on the button labeled "Add" will display the vector sum, and its components, magnitude and direction. Two auxiliary vectors are drawn (in faint blue and red) to help visualize the parallelogram; you can think of them as representing the original vectors, translated so as to perform the sum in a "tip-to-tail" fashion.

By design, there is no way to enter the components, magnitude, or direction of a vector directly: you must do it graphically, by dragging with the mouse. Hopefully, this way you will develop a good feel for what all these quantities mean graphically.