Question

Let vector u, v, w be such that |u| = 1, |v| = 2, |w| = 3.  If the projection vector v along u  is equal to that of vector w along vector u and v, w are perpendicular to each other, then find vector|u - v + w|.

Answer 1

Without loss of generality, we can assume

vector v = 2i and w = 3j

Let u = xi + yj + zk. Then

|u| = 1 ⇒ x² + y² + z² = 1   (1)

Projection of vector v along vector u = Projection of vector w along vector u