a)projects every vector onto the xy plane? b)reflect every vector on the xy plan

Question

a)projects every vector onto the xy plane?
b)reflect every vector on the xy plane?
c)rotate the xy plane by 60 degree and leaves z axis unchanged?
d)rotates xy plane by 45 degree ,then yz plane by 90 degree?

Explanation / Answer

a) projecting any vector onto x, y plane means that you kill z component so the Matrix is obviousely as follows: 1 0 0 0 1 0 0 0 0 b) reflection with respect xy plane means that yopu change the sign of z component so the Matrix is obviousely as follows: 1 0 0 0 1 0 0 0 -1 c) rotates the x,y plane (anti-clockwise) through 90degrees and leaves the z-axis alone means that x component goes to y and y component goes to x so the Matrix is obviousely as follows: 0 -1 0 1 0 0 0 0 1 d) rotates the x,y plane,then the x,z plane, then the y,z plane through 90degrees, means that every component chanes the sign and we have x -> -z, y->-y, z->-x so the Matrix is obviousely as follows: 0 0 -1 0 -1 0 -1 0 0 e) carries out the same three rotations, but each through 180degrees means that eaxh component changeed its sign twice, so effestively nothing actually happened all the components return to their original position, so the Matrix is identity 1 0 0 0 1 0 0 0 1 Hope I helped >:D

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