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)