# C4 Vectors help

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#1
http://www.examsolutions.net/a-level...ark_Scheme.pdf
http://examsolutions.net/a-level-mat...0&solution=5.2
http://examsolutions.net/a-level-mat...e/paper.php#Q5

I need help on q5b please. I thought it was a general rule that whenever you are interested in the angle between two vectors, the 2 vectors MUST be pointing away from the angle, with their "tails" at the angle? Sorry hard to describe by words. Hopefully the images show what I'm trying to say. Why/how do you get the same final answer despite not following this rule like the MS and the Examsolutions guy did?

Thanks a lot.
0
6 years ago
#2
What are you confused about? The fact you use PO and the mark scheme used OP and you both ended up with the correct answer? It's because PO and OP are both perpendicular to l_1, so it doesn't really matter which way you have the vector going.
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#3
(Original post by Jooooshy)
What are you confused about? The fact you use PO and the mark scheme used OP and you both ended up with the correct answer? It's because PO and OP are both perpendicular to l_1, so it doesn't really matter which way you have the vector going.
But the book said like in the image that the direction matters though. So the book is wrong then?
0
6 years ago
#4
(Original post by krisshP)
But the book said like in the image that the direction matters though. So the book is wrong then?
There are always two angles between any pair of intersecting straight lines in 2D and these angles add up to 180 degrees.

If you draw both vectors pointing away from the point of intersection, or both pointing into the point of intersection, when you work out the dot product you should always get the same value for the cosine of the angle so you get a consistent angle.

If you reverse the direction of one of the vectors, the dot product comes out with the opposite sign which means the cosine has the opposite sign too and you're calculating the supplementary angle instead.
0
6 years ago
#5
(Original post by krisshP)
http://www.examsolutions.net/a-level...ark_Scheme.pdf
http://examsolutions.net/a-level-mat...0&solution=5.2
http://examsolutions.net/a-level-mat...e/paper.php#Q5

I need help on q5b please. I thought it was a general rule that whenever you are interested in the angle between two vectors, the 2 vectors MUST be pointing away from the angle, with their "tails" at the angle? Sorry hard to describe by words. Hopefully the images show what I'm trying to say. Why/how do you get the same final answer despite not following this rule like the MS and the Examsolutions guy did?

Thanks a lot.
If both vectors point towards the angle then the result will be the same.
0
#6
I visualised the situation and now understand how the mark scheme method ends up working.

Thanks.
0
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