Exciting Vector Mathematics!

What is the magnitude of vector c?

Given vectors a and b, what is the magnitude of vector c where c = a + b?

Answer:

The magnitude of vector c is sqrt(4x^2 + 49y^2).

To find the magnitude of vector c = a + b, we can use the Pythagorean theorem in two dimensions, where the magnitude of a two-dimensional vector (a, b) is given by:

|c| = sqrt(a^2 + b^2)

First, we find the components of vectors a and b:

a = 4x + 5y

b = -2x + 2y

Adding these vectors gives:

c = a + b = (4x + 5y) + (-2x + 2y) = 2x + 7y

Now, we can find the magnitude of vector c using the Pythagorean theorem:

|c| = sqrt((2x)^2 + (7y)^2) = sqrt(4x^2 + 49y^2)

Therefore, the magnitude of vector c is sqrt(4x^2 + 49y^2).