Question

Cross Product of Vectors. definition and example

Answer 1

Cross product is the method you use to multiply two vectors.

General formulas of a cross product (axb):

`\begin{gathered} a(a_x,a_y,a_z) \\ b(b_x,b_y,b_z) \\ \\ a* b=c \\ \\ c_x=a_yb_z-a_zb_y \\ c_y=a_zb_x-a_xb_z \\ c_z=a_xb_y-a_yb_x \\ \\ c(c_x,c_y,c_z) \end{gathered}`

Example:

Multiply the next vectors:

a(5,2,-3)

b(-1,-4,7)

`\begin{gathered} a* b=c \\ \\ c_x=2*7-(-3)*(-4) \\ c_x=14-12 \\ c_x=2 \\ \\ c_y=(-3)*(-1)-5*7 \\ c_y=3-35 \\ c_y=-32 \\ \\ c_z=5*(-4)-2*(-1) \\ c_z=-20+2 \\ c_z=-18 \\ \\ a* b=(2,-32,-18) \end{gathered}`