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# Vectors and similar triangles question

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1. 'Use similar triangles to explain why the vectors (5, 2) is perpendicular (at right angles) to the vector (4, -10)'

I've been getting confused about this question for a while. I've drawn the triangles but I'm not quite sure how to use them to explain it...
2. (Original post by petrus123)
'Use similar triangles to explain why the vectors (5, 2) is perpendicular (at right angles) to the vector (4, -10)'

I've been getting confused about this question for a while. I've drawn the triangles but I'm not quite sure how to use them to explain it...
Vector [4,-10] is the same as vector [2,-5] (same direction, less magnitude) which is where a similar vector triangle is created. Can you see the link from there?
3. (Original post by RDKGames)
Vector [4,-10] is the same as vector [2,-5] which is where a similar vector triangle is created. Can you see the link from there?
I understand that much, but how can you explain they are perpendicular (sorry for being dopey)?

EDIT: I know that the fact one of the vectors is reversed makes them perpendicular, but I don't know how to explain it or how I'm meant to answer the question.
4. (Original post by petrus123)
I understand that much, but how can you explain they are perpendicular (sorry for being dopey)?

EDIT: I know that the fact one of the vectors is reversed makes them perpendicular, but I don't know how to explain it or how I'm meant to answer the question.
If you were to join the triangles you can use ratios and angles to prove perpendicularity.
5. (Original post by RDKGames)
If you were to join the triangles you can use ratios and angles to prove perpendicularity.
OK, I'll try that. Thanks :-)
6. (Original post by petrus123)
OK, I'll try that. Thanks :-)
Does this work?
Attached Images

7. (Original post by petrus123)
Does this work?
You haven't shown they're similar so you haven't used that fact.
8. (Original post by RDKGames)
You haven't shown they're similar so you haven't used that fact.
How would you 'show they're similar'? Just add that 5/2 = 10/4 = 2.5?
9. (Original post by petrus123)
How would you 'show they're similar'? Just add that 5/2 = 10/4 = 2.5?
By showing that the vector where k is a constant. Then proceeding to draw the [2,-5] vector triangle alongside the [5,2] one. Then using angles and ratios to prove what you need.
10. (Original post by RDKGames)
By showing that the vector where k is a constant. Then proceeding to draw the [2,-5] vector triangle alongside the [5,2] one. Then using angles and ratios to prove what you need.
Thanks.
Do you need to do all three? Isn't the first sufficient (if the x to y ratio is the same, the angle will be the same).

Is the third step what I did (in the picture) or is that wrong?
11. (Original post by petrus123)
Thanks.
Do you need to do all three? Isn't the first sufficient (if the x to y ratio is the same, the angle will be the same).

Is the third step what I did (in the picture) or is that wrong?
It would be enough if they didn't ask for similar triangles as part of the explanation.
12. (Original post by RDKGames)
It would be enough if they didn't ask for similar triangles as part of the explanation.
Thanks. I think I get it now. Is this the right sort of answer?
Attached Images

13. (Original post by petrus123)
Thanks. I think I get it now. Is this the right sort of answer?
Yeah... "sort of". You need to get the vector right with the correct signs and use that vector's similar triangle in your working out. This is nothing complicated.
14. (Original post by RDKGames)
Yeah... "sort of". You need to get the vector right with the correct signs and use that vector's similar triangle in your working out. This is nothing complicated.
I'm aware. I think I'm missing the obvious.

Isn't flipping the triangle necessary to show it's a right angle? Otherwise, what would you try to show with the similar triangles?

Thanks, and sorry this is taking me so frustratingly long!
15. (Original post by petrus123)
I'm aware. I think I'm missing the obvious.

Isn't flipping the triangle necessary to show it's a right angle? Otherwise, what would you try to show with the similar triangles?

Thanks, and sorry this is taking me so frustratingly long!
Of course not. What do you mean? You are missing the obvious because you are not using the similar triangle to [4,-10] when you join up the two distinct vector triangles.

The thing with the similar triangle is that it clearly shows how that vector is related to the other one (from using the same numbers) so from there on in you should be able to prove it without much hassle.
16. (Original post by RDKGames)
Of course not. What do you mean? You are missing the obvious because you are not using the similar triangle to [4,-10] when you join up the two distinct vector triangles.

The thing with the similar triangle is that it clearly shows how that vector is related to the other one (from using the same numbers) so from there on in you should be able to prove it without much hassle.
I'm getting very confused at this point. How would adding a similar triangle help me to prove this, and where and what size would it be? Any chance you could draw a quick sketch (MS Paint)? Again, I have a feeling I'm going to kick myself, but I just don't get what I'm trying to do...
17. (Original post by petrus123)
I'm getting very confused at this point. How would adding a similar triangle help me to prove this, and where and what size would it be? Any chance you could draw a quick sketch (MS Paint)? Again, I have a feeling I'm going to kick myself, but I just don't get what I'm trying to do...
Just literally this alongside your previous working where you show similarity. Here you can show which angles are the same and work from there.

18. (Original post by RDKGames)
Just literally this alongside your previous working where you show similarity. Here you can show which angles are the same and work from there.

Thanks for the drawing and the help. Is the point of that just to show the angles (which weren't clear on my drawings)?

Like this? (also the question sheet used parantheses for vectors and I know I forgot the arrows on the bottom part)

Sorry for being such a numpty with this problem...
Attached Images

19. (Original post by petrus123)
Thanks for the drawing and the help. Is the point of that just to show the angles (which weren't clear on my drawings)?

Like this? (also the question sheet used parantheses for vectors and I know I forgot the arrows on the bottom part)

Sorry for being such a numpty with this problem...
Yes. When working with similar triangles the angles remain the same. One triangle is simply an enlargement and/or rotation of the other.
20. (Original post by RDKGames)
Yes. When working with similar triangles the angles remain the same. One triangle is simply an enlargement and/or rotation of the other.
So that is everything needed? Yes, I know the angles stay the same (that was the basis of my first drawing; it was just unclear).

Thanks so much for helping! Good luck with Maths at Loughborough. It sounds fun!

I'm not quite as **** at maths as this post makes me look (I hope!) - I got an A in AddMaths and in the top few percent in the first round of a UK competition; I just didn't know what the question wanted and missed a couple of things...

Thanks again!

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