Thread: 2 by 2 determinant

if i have to find the cross product of a vector, lets say
u=5i -2j
v=3i-4j

is it just -20i +6j? i know how to do a 3 by 2 but without a z term i don't know how to solve it. could i just add in two 0's for z and then solve the 3 by 2?

could i just add in two 0's for z and then solve the 3 by 2?

The cross product is only defined for 3-D vectors and hence 3x3 matrices. So you do just as you suggested treat each vector as having 0 z components.