Introduction to Graphics Math

A: ()
B: ()
C: ()

When you project a vector onto another, you're taking the portion of the first vector that lines up with the second. Here, we're projecting A onto B, which yields C. To project one vector onto another, the second must be normalized. We then use the dot product of the first vector and the normalized second vector to find the magnitude of the new projected vector. Then multiply that magnitude by the normalized vector to get the final projected vector. \[\textbf{C}=(\textbf{A} \cdot \hat{\textbf{B}}) \cdot \hat{\textbf{B}}\] \[\hat{\textbf{B}}=(-0.555,0.832)\] \[\textbf{A} \cdot \hat{\textbf{B}}=1.941\] \[\textbf{C}=-1.941 \cdot (-0.555,0.832)\] \[=\underline{\underline{(-1.077,1.615)}}\]

Things to try:

• Drag A so it is in the same line as B. Notice that A is now the same as C since all of A can be projected onto B.
• Drag B so it is on the x-axis. Notice that C now has the same x value as A.
• Drag B so it is on the y-axis. Notice that C now has the same y value as A.