Final answer:
The component form of the vector with a direction angle of 287 degrees and a magnitude of 11 is approximately (3.216, -10.5193), found using the cosine and sine of the angle for the x and y components respectively.
Step-by-step explanation:
To find the component form of a vector with a direction angle of 287 degrees and a magnitude of 11, use trigonometric functions based on the angle given. For the x-component (horizontal), use cosine, and for the y-component (vertical), use sine.
The expressions will look like this:
x-component = magnitude × cos(angle)
y-component = magnitude × sin(angle)
Since the angle is measured counter-clockwise from the positive x-axis, a 287-degree angle indicates the vector is in the fourth quadrant, where the x-component is positive and the y-component is negative.
Component form calculations:
x-component = 11 × cos(287°) = 11 × cos(-73°)
≈ 11 × 0.2924
≈ 3.216
y-component = 11 × sin(287°)
= 11 × sin(-73°)
≈ 11 × -0.9563
≈ -10.5193
Therefore, the component form of the vector is approximately (3.216, -10.5193).