Find the scalar and vector projections of b on a,

where a = 2i - 5j + k, and b = -3i + 2j - 4k.

The Scalar Projection of b on a is b cos q , the component of b along a:

. Here this becomes

The Vector Projection of b on a is the component of b along a times a unit vector in the direction of a:

. Here this becomes