Difference between multiplication, dot product, and cross product symbols

Question

What is the difference between the symbols for multiplication, dot product, and cross product symbols? How can we tell them apart?

Answer 1

Often, the exact same symbol is used. You have to pay attention to context:

• When you see $$ x \times y $$ and $x,y$ were defined to be vectors, it's cross product. On the other hand if $x,y$ were defined to be numbers, it's multiplication. (For that matter, the kind of multiplication depends on the kind of number they are.)

• When you see $$ x \cdot y $$ and $x,y$ were defined to be vectors, it's dot product. On the other hand if $x,y$ were defined to be numbers, it's again multiplication.