Question
A vector in the xy plane has a magnitude of 25 and an x component of 12. The angle it makes with the positive x axis is:
A vector in the xy plane has a magnitude of 25 and an x component of 12. The angle it makes with the
positive x axis is:
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Koala Tutor
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tan θ = y/x
tan θ = y/12
Since the magnitude of the vector is 25, we can use Pythagorean theorem to find the y component:
25^2 = 12^2 + y^2
625 = 144 + y^2
y^2 = 481
y = √481
Now substitute y back into the tan θ equation:
tan θ = √481 / 12
θ ≈ 76.69 degrees
So, the angle the vector makes with the positive x axis is approximately 76.69 degrees.
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