Question

) Determina el producto vectorial: D x A= ?
D = ( 4, 5, 1) A = ( 2, -3, 3)

Answer 1

El producto cruz o vectorial entre dos vectores está dado por:

$\left(u_1,\:u_2,\:u_3\right)\times \left(v_1,\:v_2,\:v_3\right)=\left(u_2v_3-u_3v_2,\:u_3v_1-u_1v_3,\:u_1v_2-u_2v_1\right)$

$\begin{pmatrix}4,&5,&1\end{pmatrix}\times \begin{pmatrix}2,&-3,&3\end{pmatrix} = \begin{pmatrix}5\cdot \:3-1\cdot \left(-3\right),&1\cdot \:2-4\cdot \:3,&4\left(-3\right)-5\cdot \:2\end{pmatrix}$

$\begin{pmatrix}4&5&1\end{pmatrix}\times \begin{pmatrix}2&-3&3\end{pmatrix}=\boxed{\begin{pmatrix}18&-10&-22\end{pmatrix}}$