Final answer:
The direction of the sum of vectors t, u, and v can be found by calculating the horizontal and vertical components of each vector, summing these components, and then using the arctangent function to find the direction of the resultant vector.
Step-by-step explanation:
To find the direction of the sum of the vectors t, u, and v, we first need to calculate the horizontal (x) and vertical (y) components of each vector. Then we add up all the x-components and y-components to find the components of the resultant vector. Finally, we can determine the direction of the resultant vector using trigonometry.
For vector t with magnitude 5 and direction 250°, the components are:
For vector u with magnitude 6 and direction 60°, the components are:
For vector v with magnitude 12 and direction 330°, the components are:
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- vx = 12 cos(330°)
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- vy = 12 sin(330°)
Adding the components together, we get:
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- Rx = ℓx + ux + vx
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- Ry = ℓy + uy + vy
The direction θ of the resultant vector is given by θ = atan(Ry/Rx). After calculating and finding the resultant direction, round the result to the nearest degree to get your answer.