Engr Help

Vector Product

In a Nut Shell: The vector product of two vectors results in a new vector

perpendicular to the original two vectors. The direction of the new vector is

conveniently determined using the “right hand rule”.

For a rectangular coordinate system point the fingers of your right hand in the direction of

the x-axis. Then rotate your fingers towards the y-axis. The result of a vector product is

another vector (your thumb) perpendicular to the two original vectors (along the z-axis).

See the figure below.

The vector product, also called the cross product, of U = (u₁,u₂,u₃) and

of V = (v₁, v₂, v₃) is define by the 3 x 3 determinant below as:

i j k

U xV = det u₁ u₂ u₃

v₁ v₂ v₃

with i , j , k in the first row u₁, u₂,u₃ in the second row, and v₁, v₂,v₃ in the third row