Question

Decompose the vector w into a sum of its vectors in its parallel and perpendicular components. The vector w is described as 3 in the x direction and -4 in the y direction. The parallel component of the x vector should be in the direction of the vector u and the perpendicular component of vector w is perpendicular to vector u. The vector u is described as 1 in the x direction and 2 in the y direction.

Answer 1

The w and u vectors are depicted above. The green vector represents the vector component of w parallel to u and red vector represents the vector component of w perpendicular to u. We intend to find them.

where,

The perpendicular component w1 is given as

This is the component of w parallel to u and it points in the direction of unit vector of u.

Now,

The component of w perpendicular to u is given as

Where |w2| is the vector component of w perpendicular to u and