Calculate ((i + j) × (j + k)) · (i + k), if it exists

Question

Calculate ((i + j) × (j + k)) · (i + k), if it exists. If it does exist, show all your steps and explain what the result means geometrically. If it does not exist, explain in detail why it does not exist.

Answer 1

(i + j) x (j + k) = i x j + i x k + j x j + j x k = k - j + 0 - i = k - i - j

(k - i - j) · (j + k) = 0 + 1 - 0 - 0 - 1 - 0 = 0

Answer: 0