Scaling Vectors Investigation On graph paper, you will be lengthening and shrinking vectors that have a Cartesian, [x, y], representation and then adding them together. Before you begin, take some time to think about what will happen to the components if the magnitude is scaled. During the investigation, you can work to either confirm your hypothesis or understand why your hypothesis was incorrect. Note If you don't have graph paper available, use electronic graphing software like GeoGebra. Procedure 1. Draw out two separate scales with an c-axis and a y-axis, with the origin at the center. Choose a comfortable range of values for your paper, perhaps from -20 to +20 on the z and y axes. 2. On each set of axes, draw out a position vector. These vectors will be lengthened, so make sure to leave some room to grow on your paper. 3. Label the first position vector as @A and label its vector coordinates [x, y]. Label the second vector as @) and label its vector coordinates as well. 4. Choose a ratio or a number to lengthen your vectors by. These may be two different numbers. Choosing 2 or 3 are easy choices, but you can also lengthen by a factor such as 50%. In this case, you would use 1.5 as your number. For reference, I will call your numbers s and t. 5. Lengthen your vectors by measuring their original magnitudes and multiplying those magnitudes by your numbers s and t respectively. The direction of the lengthened vectors should be the same as the originals. Record the new *, y] coordinates for each vector, SO Aand tOB. 6. On one set of axes, add SOA and tOB head to tail and record the [*, y] coordinates of the sum. On the other set of axes, add OA and QB and record the coordinates of the sum as well