A dot stands for multiplication simply because nothing else in math is a dot. Since X is a common math variable it is not used very often anymore in because it is too confusing when the problem looks like 3x x x + x= it is very hard to decipher.
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They give us different results. The dot product produces a number, while the scalar multiplication produces a vector.
multiplication
The dot method is a multiplication method used in Vedic Mathematics. It is done by multiplying the different numbers in a weird type of fashion.
Why algebra has a different multiplication sign is because they don't want to mix up the American multiplication sign with the variable x. So they use a centered dot for algebra instead of this: x.
parentheses exponents multiplication addition subtraction