Vector Projections in 2D by Mohamed Habib

Imagine it's a clear day and the sun is shining down upon the Earth. Let's pretend that the line containing vector v is the ground. Let's pretend that vector u is a stick with one endpoint on the ground and one endpoint in the air. Since the sun is shining brightly, vector u would therefore cast a shadow on the ground, no? The projection of u onto v is another vector that is parallel to v and has a length equal to what vector u's shadow would be (if it were cast onto the ground). Instructions: - Move the three white dots to change the vector u and v's components. - Drag the "slide me" slider to the right to cast the Projection (shadow). - On the right side you will see how to compute the Vector projection in details. - Manually try one on your own and then check the answer. - Is the Projection a vector or a scalar? - what if both vectors are Orthogonal? Write down your own notes about the subject.