M1 vectors Watch

Mos Def
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#1
Report Thread starter 11 years ago
#1
How do i go about calculating negative angles such as:

Find the magnitude of the vector and the angle it makes with Ox.

The vector is: -2i - 3j , the mag is 3.61, and the angle is -123.7, i try to use tan and get tan^-1 (3\div 2) which gives 56.3 and is wrong.
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generalebriety
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Report 11 years ago
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Draw a diagram? 56.3 isn't "wrong", you've just found the wrong angle.

(Incidentally, I disagree with the given answer: I'd say it was -124.)
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Mos Def
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#3
Report Thread starter 11 years ago
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Crap i always do that with the answer...yeah your right. Ok i drew the diagram...



I dnt get what 0x means... i think 0x meant the angle i drew in green, but that certainly doesnt get me 123.7.
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generalebriety
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No, Ox is some rather sloppy notation for "the positive x-axis", O obviously being the origin. So you actually want the obtuse angle corresponding to that green angle. Draw it on a pair of axes from the origin and you'll see which angle it means.
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Mos Def
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#5
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ahh ok i did cos^-1 (-2/3.6) = 123.7, but its not negative ...am i meant to just add that? And for confirmation, does the 'vector' mean the hypotenuse line it makes?
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generalebriety
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#6
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Yes to your second question. Yes and no to your first. No, because what you've worked out is the angle between Ox and -2i + 3j. Angles are generally measured anticlockwise from the x-axis, so if you have to go clockwise to get to the vector, your angle will be negative. (Of course, this means that 236.3 is an equally good answer. It's just much neater to give it as an angle between -180 and +180.) But yes because there's no way you'll get the cos-1 function to give you a negative answer anyway (as the range of this function is 0 < cos-1 x < 180 degrees).

Edit: sorry, there's me using C3 terminology. By "the range of this function", I mean "the values that cos-1 x can have".

(Edited because I was being stupid. :p:)
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Mos Def
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#7
Report Thread starter 11 years ago
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Ahh i see, so just because im going anti- clockwise, im saying - 123.7? And thanks alot! I was weary about the vector being the hyp or not lol
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