Find the component form and magnitude of the vector w that has initial point(-8,-12) and terminal point (4,1)

w = <4,1> - <-8,-12> = <12,13>

Now just convert back to polar form.

To find the component form of a vector, we subtract the coordinates of the initial point from the coordinates of the terminal point.

Given that the initial point is (-8, -12) and the terminal point is (4, 1), we can find the components as follows:

The x-component is found by subtracting the x-coordinate of the initial point from the x-coordinate of the terminal point:
x-component = 4 - (-8) = 12

The y-component is found by subtracting the y-coordinate of the initial point from the y-coordinate of the terminal point:
y-component = 1 - (-12) = 13

Therefore, the component form of the vector w is (12, 13).

To find the magnitude of the vector w, we can use the formula:

Magnitude = √(x-component^2 + y-component^2)

Substituting the values:
Magnitude = √(12^2 + 13^2)
Magnitude = √(144 + 169)
Magnitude = √(313)
Magnitude ≈ 17.69

Therefore, the magnitude of vector w is approximately 17.69.