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Find an equation of the plane with the given characteristics. The plane contains the y-axis and makes an angle of 3 with the positive x-axis.

User Banoffee
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1 Answer

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Final answer:

The equation of the plane is -cos(3)x + sin(3)y = 0.

Step-by-step explanation:

The equation of the plane can be found using the normal vector of the plane and a point that lies on the plane. Since the plane contains the y-axis, a point on the plane can be taken as (0, 1, 0) (assuming a 3-dimensional coordinate system). The angle the plane makes with the positive x-axis is 3 radians (assuming standard units). The direction vector of the x-axis is (1, 0, 0).

To find the normal vector, we can rotate the direction vector of the x-axis by 3 radians in the counterclockwise direction. This can be done by using a rotation matrix. After rotation, the normal vector becomes (-cos(3), sin(3), 0).

Therefore, the equation of the plane containing the y-axis and making an angle of 3 with the positive x-axis is:

-cos(3)x + sin(3)y = 0

User Jhkuperus
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