Question

 Find the scalar and vector projections of b onto a .

Answer 1

Step 1:

The vectors are and .

Scalar projection of onto is .

Find the dot product of the vectors and .

If  and are two vectors, then the dot product of and is

The dot product of the vectors and is

Magnitude of the vector is .

Substitute and in the scalar projection formula.

.

Step 2:

Vector projection of onto is .

Substitute , and in the vector projection formula.

Vector projection of onto is

.

Solution:

Scalar Projection of onto is

Vector projection of onto is .