Find both the scalar and vector projection of
vector u = <1, 1, 1> in the direction of vector v = <1,-1,1>

Answer.
v-hat = unit vector in vector v direction is v/|v|. Since |v|= sqrt(3),
v-hat = <1/sqrt(3), -1/sqrt(3), 1/sqrt(3)>

The scalar projection is u dot v-hat = 1/sqrt(3) - 1/sqrt(3) + 1/sqrt(3) 
= 1/sqrt(3)

The vector projection is the scalar projection times v-hat or
(1/sqrt(3))<1/sqrt(3), -1/sqrt(3), 1/sqrt(3)> = <1/3, -1/3, 1/3>