Can I use a fraction of vector to reverse cross product?
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite The cross product is defined by the formula $$ vec A_i times vec B_j = |A|,|B| sinalpha = vec C_k tag1$$ Where $alpha$ is angle between vectors $A$ and $B$. $C$ is a pseudovector perpendicular to $A$ and $B$. And i, j, k is standard basis direction mutually perpendicular to each other. Assuming $alpha$ it equals $90$ degrees then $sin90=1$. This discussion is only for this case. Reverse cross product we encounter for a problem $$ vec C_k times vec A_i = vec B`_j tag2$$ The $B`$ vector has the correct direction but its value usually not equal $B$, because use $(1)$ $$ left(|A| , |B|right)_k times vec A_i =|A|^2 , |B| = vec B`_j tag3$$ but using the proportion $(1)$ we can easily reverse them $$AB=C rightarrow B=Cover A tag4$$ If we find the inverse of the vector $A$, we can in this case when $alpha=90$ degrees reverse cross product. How to get a vector $1/A$? The value of the vector is $$|A|= sqrta_x^2 + a_y ^2 + ...