What are the necessary and sufficient conditions that 2 vect

What are the necessary and sufficient conditions that 2 vectors in R³define a plane. (hint 1: What does it mean to share a vertex? hint 2: two parallel vectors can always be made to lie in the same plane.)

Solution

If the two vector are not linear or parallel they will definetely make a plane . for checking that the two vector are linear or not use A=xB where a and b are vector If you can write these two vector in a given form such that x is a scaler then these two vector are parallel .if you cant express these vector in the given form they will definetly make a plane

2nd method - If two vector are parallel their cross product must be zero