Doing vector homework, did i get the correct answer?

[hatten]

The point (1,1,1) is mirrored through the line (0+2t,0-3t,0+t). What's the mirrored point?

Answer sheet says (1,-1,-1), teachers calculations says (-1,-1,-1) and my calculations says (-1,-1,-1).

I normally wouldn't ask this, but I'm kinda unsure of my calculations, and in two of the earlier questions the Teacher's calculations was wrong while the answer sheet was correct. Anybody care to quickly calculate it and confirm whether I'm correct?

[jestingrabbit]

The point (1,1,1) is mirrored through the line (0+2t,0-3t,0+t). What's the mirrored point?

Answer sheet says (1,-1,-1), teachers calculations says (-1,-1,-1) and my calculations says (-1,-1,-1).

I normally wouldn't ask this, but I'm kinda unsure of my calculations, and in two of the earlier questions the Teacher's calculations was wrong while the answer sheet was correct. Anybody care to quickly calculate it and confirm whether I'm correct?

A necessary, but not sufficient, condition on the mirrored vector is that if you add it to the unmirrored vector, you arrive on the line. That's true of your answer and false for the books, so the book is definitely wrong.

[hatten]

Good to know, I'll keep that in mind. Thanks a lot

[jestingrabbit]

np. Its only true for lines through the origin, so watch out for that!

[skeptical scientist]

A necessary, but not sufficient, condition on the mirrored vector is that if you add it to the unmirrored vector, you arrive on the line. That's true of your answer and false for the books, so the book is definitely wrong.

np. Its only true for lines through the origin, so watch out for that!

In general, the average of a vector and its mirror will be on the line. Since the average is half the sum, for lines through the origin, this amounts to the same thing.

I also get (-1,-1,-1). The answer sheet probably just has a typo.

[hatten]

Well yeah, just realized that on the next question when i tried mirroring (0,0,0) through a line >_>