This worksheet uses two applets to explore vectors. The first applet lets you look at addition and subtraction of vectors is R^2 along with converting representations. The second applet looks at the dot and cross product.
To access the vector addition applet follow the link:
The applet opens with Vector A in green and Vector B in red. The values of these vectors can be changed by dragging the point at the tip of each vector. The upper left corner of applet gives the data on the vectors in both Cartesian and polar forms. The angle of the vector is given in degrees. The scale of the graph can be changed by dragging the unit point on the x-axis. (It is easier to move the vectors to nice points if you rescale the graph first.)
1) Give the magnitude and direction for the vectors (3,4), (5,2), and (10,7). Find the y-coordinate of a vector with direction 15 degrees and x-coordinate 10.
2) Click on the "Show A+B" button to show a translation of Vector A in light green and the vector A+B in orange.
Add the vectors (-1,2) and (4,2). Give the result in polar form.
repeat the process with (-6, 2) and (-2,6). Give the polar form of the difference of the 2 vectors.
To access the applet on dot and cross product and projections follow the link:
The applet opens with Vector A in green and Vector B in red. An area representing the dot product is in green an an area representing the cross product is in yellow. A projection vector is in blue. Click on the "hide cross product" buttons to simplify what you are looking at.3) Set vector A to (4,2). Drag vector B along the line y=4.