Angles / Vector Algebra grade 12 mathematics

[riyalass]

Okay so the image shows a common triangle ABC, for all the four cases with angle CBA = theta . And with that , we're going to find the angle between all possible pairs of vectors.

So is the below image correct? In the rhs, I've rearranged the vector pairs by extending the vectors from the diagram in lhs such that the vectors are in a tail to tail position so the angle between them can be calculated. Also is the naming of the vectors at the rhs correct which I'm pretty sure isn't but I don't get where I'm going wrong.
Also are there any other possible cases for this diagram alone? (I.e., in tri ABC, with angle B = theta)

 

[The Highlander]

Okay so the image shows a common triangle ABC, for all the four cases with angle CBA = theta . And with that , we're going to find the angle between all possible pairs of vectors.

So is the below image correct? In the rhs, I've rearranged the vector pairs by extending the vectors from the diagram in lhs such that the vectors are in a tail to tail position so the angle between them can be calculated. Also is the naming of the vectors at the rhs correct which I'm pretty sure isn't but I don't get where I'm going wrong.
Also are there any other possible cases for this diagram alone? (I.e., in tri ABC, with angle B = theta)

I have corrected the vector nomenclature for you (the angles between your vectors could have been better drawn; they're quite a bit off in some cases).

However, beyond that, I'm at a loss to understand exactly what it is you are trying to achieve here.

If you can explain better what it is you are trying to do (and what you're stuck at), I'm sure further help may be forthcoming.

Hope that helps.

 

[riyalass]

I have corrected the vector nomenclature for you (the angles between your vectors could have been better drawn; they're quite a bit off in some cases).

However, beyond that, I'm at a loss to understand exactly what it is you are trying to achieve here.

If you can explain better what it is you are trying to do (and what you're stuck at), I'm sure further help may be forthcoming.

Hope that helps.

View attachment 40008

Hey yes now I get it. Thanks a lott
So basically I was trying to find out what is the true angle formed between any 2 given vectors, when they're not given tail to tail position. So I've rearranged the vectors in tail to tail position in the right side diagrams and calculated what's the angle being formed between them

 

[The Highlander]

@riyalass

Or, if the intention is to use the sides of the triangle as your vectores, then perhaps this is what you should have drawn?

​

 

[riyalass]

@riyalass

Or, if the intention is to use the sides of the triangle as your vectores, then perhaps this is what you should have drawn?

View attachment 40009​

Yes this makes sense but I wanted to find out in the very same triangle, what is the angle formed. For example in the last case, in triangle ABC, the angle between the 2 vectors is angle CAB.
Similarly, for the first case, only if I extend the base vector side AB to B' , the true vector angle I get within the triangle is angle CBB'
So yeah..

 

[riyalass]

Yes this makes sense but I wanted to find out in the very same triangle, what is the angle formed. For example in the last case, in triangle ABC, the angle between the 2 vectors is angle CAB.
Similarly, for the first case, only if I extend the base vector side AB to B' , the true vector angle I get within the triangle is angle CBB'
So yeah..

The above image is a lot more clear btw thankyou!!