Question

How does one calculate cross products and dot products in Physics? Urgent help needed for an exam.

Answer 1

please see below

Explanation:

Dot products and cross products refer to vectors.
Dot products are also called "scalar products", because the result of a dot product is a scalar (i.e. a number), not a vector.

Lets have `vec a = (a_"1" | a_"2" | a_"3")`
and `vec b = (b_"1"|b_"2"|b_"3")`

The dot product is calculated as follows:

`vec a * vec b = a_"1"*b_"1" + a_"2"*b_"2" + c_"1"*c_"2"`

In case of cross products of two vectors the result is a vector. Therefore cross products are only applicable to three-dimensional systems.

Lets take our two vectors `vec a = (a_"1" | a_"2" | a_"3")`
and `vec b = (b_"1"|b_"2"|b_"3")`

The cross product is calculated as follows:

`vec a xx vec b = (a_"2"*b_"3"-b_"2"*a_"3"|b_"1"*a_"3"-a_"1"*b_"3"|a_"1"*b_"2"-b_"1"*a_"2")`