Cartesian Vector Addition

We're going to be doing the parallelogram rule for vector addition here, using a Cartesian Plane.

First, create a Square Grid on your GSP drawing. Go to Graph -> Grid Form -> Square Grid. Now use the line tool and create two lines that pass through the origin.

Click and hold on the line tool to see all the options . The line tool is the farthest right. Once the lines are created, select each line and construct another point on them.

Now, create a line segment from the origin to each constructed point. Change the colour of each line segment with Display -> Colour. Change the line thickness using Display -> Line Width.

Now we're going to complete the parallelogram. Select a constructed point and the other line. Go to Construct -> Parallel Line. The new lines will match the last line settings you set but don't sweat it since we're going to hide them later anyhow. Construct the intersection of the two new lines.

Next, hide the two lines (red on the above picture). Construct Line Segments to finish off the parallelogram. This next part is cosmetic but I like to change these segments to dashed lines. Click on Display -> Line Width and Colour to change these lines. Lastly, construct a segment from the origin to the opposite vertex of the parallelogram to show the resultant vector.

Now you have a dynamic way to show that vector addition works. You can alter the direction of the vectors and the length of the vectors by manipulating the points. Everything else follows along!

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