A vector in the xy plane has a magnitude of 25m and an x component of 12m. The angle it makes with the positive x axis is:Group of answer choices26 degrees29 degrees61 degrees64 degrees241 degrees
Question
A vector in the xy plane has a magnitude of 25m and an x component of 12m. The angle it makes with the positive x axis is:Group of answer choices26 degrees29 degrees61 degrees64 degrees241 degrees
Solution
The angle a vector makes with the positive x-axis can be found using the cosine of the angle, which is equal to the x-component of the vector divided by the magnitude of the vector.
The cosine of the angle θ is given by:
cos(θ) = (x-component) / (magnitude)
Substituting the given values:
cos(θ) = 12m / 25m = 0.48
To find the angle, we take the inverse cosine (cos^-1) of 0.48.
θ = cos^-1(0.48)
Using a calculator, we find that θ is approximately 61 degrees.
So, the angle the vector makes with the positive x-axis is 61 degrees.
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