Question

A light ray with direction vector v = (1, -2, -4) arrives from above and gets reflected off of the xy-plane (which acts like a mirror). Then the direction vector of the reflected ray is: w = ( , , ) Subsequently, the reflected light ray gets reflected off of the xz-plane (which also acts like a mirror). Now, the direction vector of the reflected light ray is: x = ( , , ) Check

          A light ray with direction vector v = (1, -2, -4) arrives from above and gets reflected off of the xy-plane (which acts like a mirror). Then the direction vector of the reflected ray is: w = ( , , ) Subsequently, the reflected light ray gets reflected off of the xz-plane (which also acts like a mirror). Now, the direction vector of the reflected light ray is: x = ( , , ) Check
        
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A light ray with direction vector v = (1, -2, -4) arrives from above and gets reflected off of the xy-plane (which acts like a mirror). Then the direction vector of the reflected ray is: w = ( , , ) Subsequently, the reflected light ray gets reflected off of the xz-plane (which also acts like a mirror). Now, the direction vector of the reflected light ray is: x = ( , , ) Check

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Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Alan S. Tussy, R. David Gustafson 5th Edition
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A light ray with direction vector v = (1, -2, -4) arrives from above and gets reflected off of the xy-plane (which acts like a mirror). Then the direction vector of the reflected ray is: w = ( , , ) Subsequently, the reflected light ray gets reflected off of the xz-plane (which also acts like a mirror). Now, the direction vector of the reflected light ray is: x = ( , , )
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Transcript

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00:01 In this question, we're given a vector v is equal to 1 minus 2 minus 4, and we want to find the same vector v or its direction once it is reflected about the x, y plane in question a.
00:14 And in question b, we want to know what happens to this vector once it is reflected about the xz plane.
00:22 So let's drop what's going on to help us graphically.
00:26 If we have a plane in the xy plane, and if we're given a coordinate above the xy plane, a reflection about this plane is going to give us a point below the plane of negative z.
00:54 So a reflection about the xy plane will change our z coordinates to minus z.
01:05 Therefore, our vector v will have an inbrated z direction...
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