Let . Calculate each cross product. Since , you know .
I'm finding my algebra unit quite difficult compared to calculus... Could someone help with the below problem?
Thanks in advance!Let m, n and o be three vectors in R3 such that
m + n = o.
(a) Show that m x n = o x n = m x o.
(b) Use the geometric meaning of vector addition and cross
product to explain the statement of (a) geometrically. Make
sure that all the cases are covered.
It is also the vector that is normal (or perpendicular) to the plane containing the two vectors. The vector $m+n$ is in the same plane as both $m$ and $n$, so the same vector that is perpendicular to both $m$ and $n$ will also be perpendicular with $m$ and $m+n$ and $n$ and $m+n$.