If are three non-coplanar vectors such that then show that is the null vector

Question

If  are three non-coplanar vectors such that  then show that  is the null vector

Philoid · Accepted Answer

Given that are non-coplanar and and

From above given conditions we can say that either

(i) or

(ii) is perpendicular to and

Since and are non-coplanar, cannot be simultaneously perpendicular to all three, as only three axes exist that is x, y, z

So must be a null vector which is equal to 0