If \(a >0\) is a scalar, then \(| a \vec u | = a |\vec u |\) Given any nonzero vector \(\vec u\), the vector \(\frac { \vec u } {|\vec u|} \) has magnitude 1. Suppose that \(\vec u\) and \(\vec v\) are nonzero three dimensional vectors and \(\vec u \dotp \vec v =0\). Then, \(\vec u\) and \(\vec v\) are
orthogonal. If \(\vec v\) is a unit vector and \(\vec u\) is any nonzero vector, \(\scal _{\vec v} \vec u = \vec u \dotp \vec v\). If \(\vec u\) and \(\vec v\) are
orthogonal unit vectors, then \(\vec u \cross \vec v\) is a unit vector.
Remember that \(\proj _{\vec v} \vec u\) is in the direction of \(\vec v\).
Since \(\vec u\) and \(\vec v\) are parallel then there is some \(c\) such that \(\vec u = c \vec v\).
Remember that \(\vec u \times \vec v\) is orthogonal to both \(\vec v\) and \(\vec u\).