Are the vectors #u=<1, -2># and #v=<4, 8># parallel, orthogonal, or neither?
Neither parallel nor orthogonal. The angle between the two vectors is:
Compute the dot-product:
We computed the dot-product by multiplying the respective components of the vectors. Another definition of the dot-product is the magnitudes of the vectors multiplied by the angle between them:
Compute the magnitudes of the two vectors:
Substitute the values for the dot-product and the magnitudes into equation :