# C4 VectorsWatch

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#1
Three points A,B and C have position vectors OA=3i-2j+k , OB=-1i+j-3k , OC=2i-5j+3k. Find the angles of the triangle ABC in degrees. Here is my attempt to this question I found the vectors AB,BC and CD using the position vector of each. I then used scalar product formula between AB and AC ,did the same for BC and CA, BC and BA. The sum of 3 angles I got which are supposed to be sum of angles between each vector is way greater than 180. Can someone provide me an explanation for why my method didn't work and alternative way of doing this pls.
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5 years ago
#2
(Original post by Merdan)
Three points A,B and C have position vectors OA=3i-2j+k , OB=-1i+j-3k , OC=2i-5j+3k. Find the angles of the triangle ABC in degrees. Here is my attempt to this question I found the vectors AB,BC and CD using the position vector of each. I then used scalar product formula between AB and AC ,did the same for BC and CA, BC and BA. The sum of 3 angles I got which are supposed to be sum of angles between each vector is way greater than 180. Can someone provide me an explanation for why my method didn't work and alternative way of doing this pls.
This should have worked - what angles did you get?
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#3
(Original post by Smaug123)
This should have worked - what angles did you get?
Well I got first two angles to be 57 degrees and 143 degrees unless I made a mistake on working out which I don't think I have..
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5 years ago
#4
(Original post by Merdan)
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Make sure at OA, you are using the vectors AB and AC.

At OB, use vectors BA and BC. At OC, use vectors CA and CB.

1
5 years ago
#5
(Original post by Merdan)
Well I got first two angles to be 57 degrees and 143 degrees unless I made a mistake on working out which I don't think I have..
Can you write your working for the A vertex? I make the angle at A to be 92.8 degrees, and my three angles add up to 180.

EDIT: Oops, I misread the question and used b=(-1,1,3) rather than (-1,1,-3). Re-working to check consistency with pleasedtobeatyou…

EDIT 2: I agree with pleasedtobeatyou above.
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#6
Make sure at OA, you are using the vectors AB and AC.

At OB, use vectors BA and BC. At OC, use vectors CA and CB.

Looking at your work I see that when you are considering a particular angle you have used your direction of other two vectors pointing outwards as for angle A you have considered AB and AC whereas I used AB and CA I guess that's why I am not getting consistent hence get different a.b for the same modulus A x Modulus B costheta ....
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5 years ago
#7
(Original post by Merdan)
...
Yes because the in the dot product refers to the angle between two vectors. For instance, the angle between AB and AC is different from the one between AB and CA.
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