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I've recently gotten into physics, since I wanted to start learning it after I self-studied Calculus 1. I'm currently using the textbook "Fundamentals of Physics" by Halliday, however, I'm having a bit of a problem with vectors.

I think I have a bit of an intuitive understanding with the dot product, but not a strong one. On the note of cross product, I'm pretty clueless on how it works intuitively with the use of the right-hand rule.

I was wondering if someone could point me to any resources or give me an explanation that could try and give me a stronger intuitive sense for both? Thank you in advance.

Academia
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1 Answers1

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I find that the geometric intuition behind vectors and vector operations is very helpful in conceptually understanding what they mean.

You can think of the dot product as the product of the magnitude of one vector and the magnitude of the component of the other vector pointing along the same direction as the first vector (and vice versa).

The cross product is very similar, except its result is a vector which is perpendicular to both of the input vectors. The right-hand rule is a way to determine which way the resultant vector will point. Geometrically, the cross product of two vectors gives the area of a parallelogram formed by the input vectors. This is the opposite of the dot product, which is a measurement of how closely two vectors align.

There's a YouTube playlist by 3Blue1Brown which provides a very good intuitive understanding of basic linear algebra concepts, I'll link it here: Essence of Linear Algebra.

DanDan0101
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