Answer:
- u = <-0.7237, 5.1494>
- v = <3.8450, 1.1025>
The decimal values are approximate. Round the values however your teacher instructs.
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Step-by-step explanation
The vectors are displayed using their length (aka magnitude), and their angle.
The goal is to determine the <x, y> form of the vector.
I'll be using these two formulas
- x = r*cos(theta)
- y = r*sin(theta)
For vector u, we have r = 5.2 and theta = 98 degrees
- x = r*cos(theta) = 5.2*cos(98) = -0.7237
- y = r*sin(theta) = 5.2*sin(98) = 5.1494
The two results are approximate. Round the values however your teacher instructs. Your calculator needs to be in degree mode.
The component form of vector u is approximately <-0.7237, 5.1494>
It means we move about -0.7237 units in the x direction (this amount to the left), and also 5.1494 units in the y direction.
Through similar steps, vector v will have:
- x = r*cos(theta) = 4*cos(16) = 3.8450
- y = r*sin(theta) = 4*sin(16) = 1.1025
The component form of vector v is approximately <3.8450, 1.1025>