If llull=1 and llvll=3, and the vectors maek angles of 170 degrees and 130 degrees with the x-axis respectively, find the component form of the sum of u and V.
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To find the component form of the sum of vectors u and v, we need to determine their x and y components.
Given that the vector u makes an angle of 170 degrees with the x-axis and the vector v makes an angle of 130 degrees, we can use trigonometry to find their x and y components.
To find the x-component of u, we can use the formula:
x-component = magnitude * cos(angle)
Since the magnitude of vector u is given as llull = 1, and the angle with the x-axis is 170 degrees, we can calculate the x-component of u as:
x-component of u = 1 * cos(170 degrees)
Similarly, to find the y-component of u, we use the formula:
y-component = magnitude * sin(angle)
So, the y-component of u is:
y-component of u = 1 * sin(170 degrees)
Now let's perform the same calculations for vector v.
The x-component of v is:
x-component of v = llvll * cos(angle) = 3 * cos(130 degrees)
And the y-component of v is:
y-component of v = llvll * sin(angle) = 3 * sin(130 degrees)
Finally, to find the component form of the sum of u and v, we add the corresponding x and y components of the vectors:
x-component of the sum = x-component of u + x-component of v
y-component of the sum = y-component of u + y-component of v
So, the component form of the sum of u and v is:
(x-component of the sum, y-component of the sum)