Q:

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

Accepted Solution

A:
Let's define the vectors:
 U = (4.4)
 V = (3.1)
 The projection of U into V is proportional to V
 The way to calculate it is the following:
 Proy v U = [(U.V) / | V | ^ 2] V
 Where U.V is the point product of the vectors, | V | ^ 2 is the magnitude of the vector V squared and all that operation by V which is the vector.
 We have then:
 U.V Product:
 U.V = (4,4) * (3,1)
 U.V = 4 * 3 + 4 * 1
 U.V = 12 + 4
 U.V = 16
 Magnitude of vector V:
 lVl = root ((3) ^ 2 + (1) ^ 2)
 lVl = root (9 + 1)
 lVl = root (10)
 Substituting in the formula we have:
 Proy v U = [(16) / (root (10)) ^ 2] (3, 1)
 Proy v U = [16/10] (3, 1)
 Proy v U = [1.6] (3, 1)
 Proy v U = [1.6] (3, 1)
 Proy v U = (4.8, 1.6)

 Answer:
 the projection of (4,4) onto (3,1) is:
 Proy v U = (4.8, 1.6)