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 to polar form.
To find the component form of the vector and its magnitude, we can use the following formulas:
1. Component form formula:
If the initial point of the vector is (x1, y1) and the terminal point is (x2, y2), then the component form of the vector can be found using the formula:
w = (x2 - x1, y2 - y1)
2. Magnitude formula:
If the component form of the vector is w = (a, b), then the magnitude of the vector can be found using the formula:
|w| = sqrt(a^2 + b^2)
Let's calculate the component form and magnitude of the vector using the given initial and terminal points.
Given:
Initial point (x1, y1) = (-8, -12)
Terminal point (x2, y2) = (4, 1)
1. Component form:
Using the component form formula, we can find the vector w as follows:
w = (x2 - x1, y2 - y1)
= (4 - (-8), 1 - (-12))
= (4 + 8, 1 + 12)
= (12, 13)
Therefore, the component form of the vector w is (12, 13).
2. Magnitude:
Using the magnitude formula, we can find the magnitude |w| as follows:
|w| = sqrt(a^2 + b^2)
= sqrt((12)^2 + (13)^2)
= sqrt(144 + 169)
= sqrt(313)
≈ 17.68
Therefore, the magnitude of the vector w is approximately 17.68.