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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?

Sagot :

The angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

In this question,

A normal vector to the plane is any vector that starts at a point in the plane and has a direction that is orthogonal (perpendicular) to the surface of the xy plane .

The magnitude of the xy plane, hypotenuse = 25 units

The x component of the xy plane, base = 12 units

Let θ be an angle, then the angle it makes with the positive x axis is

[tex]\theta = cos^{-1}(\frac{base}{hypotenuse} )[/tex]

⇒ [tex]\theta = cos^{-1}(\frac{12}{25} )[/tex]

⇒ [tex]\theta = cos^{-1}(0.48)[/tex]

⇒ [tex]\theta = 61.3145[/tex]

Hence we can conclude that the angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

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