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

Answer 1

the general outline of solving this problem:

(1) ALWAYS. Always always always. Draw out the initial and terminal points to make a triangle

(2) find the x and y by simply counting from point to point [i.e. -1 to 1 in the x-direction is 4 units, so delta x = 4]

(3) next, plug that into the equation for finding magnitude which is √ [(Δx)² + (Δy)²]

(4) use the triangle plotted out from step 1 to find the angle created by using trig functions, like sin, cos, and tan. In this problem, use tan in order to find the angle created. Make sure to set the calculator to either degrees or radians, if indicated in the problem which one is needed.

(5) to find component form, simply multiple the Δx and Δy with the angles

Mathematical response

Δx = 12

Δy = 13

magnitude = √ [(Δx)² + (Δy)²] = √ [(12)² + (13)²] = 17.7

angle = tan^-1(13/12) = 47.29º

component form:

a = 12sin(47.29º) = 8.82

b = 13cos(47.29º) = 8.82

(8.82 î - 8.82 ĵ)

Let me know if that helps!