The discussion centers on the concept of the dot product in vector mathematics, specifically how it measures the projection of one vector onto another. The dot product is defined as A · B = |A||B|cos(α), where α is the angle between the vectors. Participants clarify that the dot product quantifies how much one vector extends in the direction of another, with practical applications in physics, such as calculating work done by a force vector over a displacement vector. The value of the dot product can indicate the relative direction of the vectors, with maximum, minimum, and zero values corresponding to parallel, opposite, and perpendicular orientations, respectively.
PREREQUISITESStudents of mathematics and physics, educators teaching vector calculus, and professionals applying vector analysis in engineering or computer graphics will benefit from this discussion.
You could be right. But presumably it depends upon what is classified as intuitive/simple.Aurelius120 said:I could be wrong. But don't all intuitive examples involving both physics and dot product that are also simple, involve forces?
Suppose a company sells five different products, call them A, B, C, D, and E. Suppose also that during a month, there were, respectively 25, 30, 15, 20, and 40 units sold, with per-unit revenues of $100, $120, $85, $140, and $135.NoahsArk said:I meant some kind of word problem example using a specific real world application to illustrate how the dot product works.
There must be a parable that covers your situation. Mathematics is a mountain. You have to start climbing to make progress. You can only sit at the bottom looking up for so long. You must have made a decision at some point to attempt this mountain, so you ought to get on with it.NoahsArk said:I meant some kind of word problem example using a specific real world application to illustrate how the dot product works.