1. The problem statement, all variables and given/known data ^ ^ ^ i = i; j = j; k = k; i = x j = y k = z So this is the result after cross multiplication. -2ij - 8ji = 6k -ik + 4ki = 5j -4jk +4kj = -8i Unfortunately I am a little confused with the 5j It seems to me that it would be -ik + 4ki = -j -4j because I comes first and so it would be -5j I know this is not the case but it ruins the logic of the whole ordeal for me ; /. How are you supposed to know which sign you need to flip? I thought it was if it was ij you would leave it alone but if it was ji it would be -ji because order changed and i is multiplied first.