What gives the product of 2 vectors in 2D space?

Question

Mathematics

What exactly does the product of 2 vectors give us in 2-dimensional space? Only a request to explain the essence and meaning (for what and how it can be used in practice) in an understandable simple language, and not just a "scalar" for example). Thank you.

Answer 1

The scalar product gives the projection of one vector onto another. In other words, you get the length of one vector in the direction of another.
For example, you are driving a cart. A cart of mass 1 kg moves forward with an acceleration a, and you pull it at an angle of 30 degrees to the ground with a force f = 10 newtons. This means that the trolley, roughly speaking, has an acceleration of movement 'a*f=|'a|*|f|*Sin(30) = 5 newtons.

Answer 2

For normalized vectors (having length 1), reflects the angle between the vectors (the arc cosine). We got 0 - the vectors are perpendicular, 1 - they look in one direction, -1 - in the opposite direction.

Answer 3

en.onlinemschool.com/math/library/vector/multiply1

Answer 4

In 2D there are two products of vectors (x,y) and (x',y').
• Scalar xx' + yy'. Projection of one onto the other, multiplied by the length of the other. It is zero if the vectors are perpendicular.
• Oblique xy' − x'y. The area of ​​the parallelogram on these vectors. It is zero if the vectors are collinear.