Parallel Vectors in 3D

Which of these vectors are parallel?

• Why?

• What makes them parallel?

• What are the rules here?

Algebraic Example

• For a real scalar r>0, vectors v and z are parallel if and only if v = <a,b,c> and z=r*<a,b,c>

• z=<r*a,r*b,r*c>

• if any of the components can not be equated with r*<a,b,c> then the vectors are not parallel.

Three vertices of a parallelogram ABCD are A(3,-1,2), B(1,2,-4) and C(-1,1,2). Find the coordinate of the fourth vertex. Use Geogebra 3D to help you! PROVE WHY IT MUST BE TRUE