I am self studying linear algebra to get ahead before I take it in college, and I found something in the textbook that I'm using and on Khan Academy that has confused me and brought my self learning to a screeching halt.
The following image has been taken from Gilbert Strang's Introduction to Linear Algebra
Prior to this image it saids that when vectors $v$ and $w$ are perpendicular, they form two sides of a right triangle. The third side is $v-w$ (the hypotenuse going across in Figure 1.8) Which is the image I posted. I don't understand how $v-w$ is the hypotenuse. Intuitively, it makes no sense.
In addition, I also watched the Khan Academy Video on this topic, and found that around $2:00$ into the video Sal draws a similar picture and I have no idea how the vector $a-b$ was positioned where it was.
What is the reasoning behind Sal's and Professor Strang's diagrams?