MATH SOLVE

2 months ago

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)

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)