Question

Let v= 3i − 2j + k (or equivalently ). Find non zero vectors w and u such that each of v, w and u is orthogonal (another word for perpendicular) to the other two Make sure you demonstrate that they are each orthogonal to one another after you find them.

Answer 1

w = 1 i + 1 j - 1 k

u = 1 i + 4 j + 5 k

Explanation:

Two possible vectors are:

w = 1 i + 1 j - 1 k

and

u = 1 i + 4 j + 5 k

since they verify the rules for scalar product equal zero among them:

v * w = 3 - 2 - 1 = 0

v * u = 3 - 8 + 5 = 0

u * w = 1 + 4 - 5 = 0