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:

http://www.slu.edu./classes/maymk/SketchpadApplets/AddVectors.html

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:

http://www.slu.edu./classes/maymk/SketchpadApplets/ProjectionDotCrossProduct.html

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.Describe what happens to the blue vector (projection of B onto A) as B moves from left to right.

Describe what happens to the green box (representing the area of the dot product) as B moves from left to right.

Give the coordinates of the point where the most interesting thing happens.

Give a description of the green box in terms of the red, green and blue vectors.

4) Set vector A to (4,3) and vector B to (-4,3). Walk through the computation of the projection.

Compute the lengths of A and B.

Divide vector A by its length to produce a unit vector in the direction of A.

Compute the dot product of vector A with vector B.

Find the cos of the angle between the vectors by dividing the cross product by the lengths of A and B.

Multiply the unit vector by the cos to find the projection.

Subtract the projection from vector B to find the perpendicular component.

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Last updated By Mike May, S.J.,
January 25, 2006.