Question

what is the difference between cross and dot product? can the dot product be used to determine if vectors are collinear?

Answer 1

let a and b be two vectors making an angle theta with each other.
\[then a \times b is called cross product and a.b is called \dot product.\]

Answer 2

\[a \times b=\left| a \right|\left| b \right|\sin \theta n,where n ia unit vector perpendicular to both a and b\]

Answer 3

\[a.b =\left| a \right|\left| b \right|\cos \theta \]

Answer 4

thanks
in what way is n multiplied to the cross formula? simple multiplication?

Answer 5

when the vectors are collinear angle between them is 0 or pi.
cos 0=1,and cos pi=-1
so it can be used as well.

Answer 6

cross product is a vector quantity.

Answer 7

I see. in contrast, dot product is a scalar quantity

Answer 8

yea