Rotate Plane: Transform z=b-y to Horizontal Plane

[julz127]

Homework Statement

using a rotation transform, show that the plane z = b - y can be transformed to the horizontal plane

\widehat{z} = \frac {b} {\sqrt{b^2 + c^2}}

Homework Equations

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The Attempt at a Solution

I just need some help understanding the question, if I could get a hint or something to point me in the right direction. By rotation transform do they mean a rotation transform matrix? it also looks like something is being normalised.

Sorry if I'm posting this in the wrong forum, it's from an assignment for a calculus class so I thought I'd put it here.

 

[Mark44]

Homework Statement

using a rotation transform, show that the plane z = b - y can be transformed to the horizontal plane

\widehat{z} = \frac {b} {\sqrt{b^2 + c^2}}

Homework Equations

^

The Attempt at a Solution

I just need some help understanding the question, if I could get a hint or something to point me in the right direction. By rotation transform do they mean a rotation transform matrix? it also looks like something is being normalised.

Sorry if I'm posting this in the wrong forum, it's from an assignment for a calculus class so I thought I'd put it here.

In the equation z = b - y, x doesn't appear, so to visualize the plane, start by sketching the trace in the y-z plane. You should get a straight line. The whole plane can be generated by letting this line sweep back and forth in the direction of the z-axis.

What angle does the normal to the plane (or a perpendicular to the trace in the y-z plane) make with the z-axis? That's the angle that the plane should be rotated to make it horizontal.

 

[julz127]

In the equation z = b - y, x doesn't appear, so to visualize the plane, start by sketching the trace in the y-z plane. You should get a straight line. The whole plane can be generated by letting this line sweep back and forth in the direction of the z-axis.

What angle does the normal to the plane (or a perpendicular to the trace in the y-z plane) make with the z-axis? That's the angle that the plane should be rotated to make it horizontal.

Thanks but I think my question is more about how to rotate it, my (poor) understanding of the question is that I apply some sort of rotation transform to get the second equation, or is the second equation the actual transform?

It's actually part of a larger question involving integrating the volume of an ellipsoid above a plane.

 

[Mark44]

Well, before you apply a rotation to your plane, you have to know how much (by what angle) to rotate it. Or equivalently, instead of rotating the plane, you could rotate the axis system the opposite direction. The new equation you showed is not the rotation transform.