What is the projection of (3, 4) onto (3, 1)?

Solution:

Given (3, 4) onto (3, 1)

Let a = 3 + 4i and b = 3 + i

The projection of a on b is given as b.a/|b|

|b| = √3² + 1² = √10

b.a = (3 + 4i).(3 + i)

= (3)(3) + (4(1))

= 9 + 4

b.a = 13

The projection is 13/√10.

What is the projection of (3, 4) onto (3, 1)?

Summary:

The projection of (3, 4) onto (3, 1) is 13/√10.