What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # ( - 5 i + 4 j - 5 k) #?
you need to calculate the vector (cross) product of these two vectors to get the normal vector
it's not clear to me how you latex matrices on here so i will draw the computation.
so the normal vector is the determinant of the matrix as shown and we get as one possible normal vector [there an an infinite number of actual formulations of this]
the unit vector is therefore