Help visualising this triangle

[charmedbeauty]

Homework Statement

I think this must be really easy but I am not getting a visual for this triangle description.

Let ABC be a triangle with \UparrowOA=a and /UparrowOB=b and /UparrowOC = c
Where O is the origin .

Homework Equations

The Attempt at a Solution

How can I have a triangle ABC where all A,B,C are sides coming from O

The way I'm looking at this is I have a point O, where the lines A,B,C start from ie, A,B,C only have one available endpoint.

So how can these lines make a triangle without introducing a new line??

Clearly, I am imagining things wrong here, I tried drawing it but it still didn't work. Help!

 

[ehild]

See attachment.

ehild

 

[charmedbeauty]

see attachment.

Ehild

thank you sir!

 

[charmedbeauty]

See attachment.

ehild

Hmm I have a question related to this triangle and it asks

i) If M is the midpoint of the line segment AB and P is the midpoint of the line segment CB express the vectors \vec OM and \vec OP in terms of a,b, and c.

ii) Show that \vec MP is parallel to \vec AC and has half its length.

Ok for part i) the answer is 1/2(b-a), 1/2(b-c), but to me it should be 1/2(b+a), 1/2(b+c)... as if you were to minus a or c does that not imply that you 'attach a/c to the end of vector b or in this case 1/2b and 1/2 (c,a)...
I think the difficulty I am having is understanding the direction in the vector, how do I know which way it is 'pointing' so to speak??

in this situation what would the addition of the vectors look like?

Thanks!

 

[Curious3141]

Hmm I have a question related to this triangle and it asks

i) If M is the midpoint of the line segment AB and P is the midpoint of the line segment CB express the vectors \vec OM and \vec OP in terms of a,b, and c.

ii) Show that \vec MP is parallel to \vec AC and has half its length.

Ok for part i) the answer is 1/2(b-a), 1/2(b-c), but to me it should be 1/2(b+a), 1/2(b+c)... as if you were to minus a or c does that not imply that you 'attach a/c to the end of vector b or in this case 1/2b and 1/2 (c,a)...
I think the difficulty I am having is understanding the direction in the vector, how do I know which way it is 'pointing' so to speak??

in this situation what would the addition of the vectors look like?

Thanks!

If your answer is that \vec{OM} = \frac{1}{2}(a + b) and that \vec{OP} = \frac{1}{2}(b + c),

then you are, in fact, right (and the book is wrong). a, b and c are position vectors - which means they define the positions of points A, B and C respectively with respect to a common origin O. By convention, they *always* point outward from the origin O toward the terminal point. So a = \vec{OA}, etc.

 

[charmedbeauty]

If your answer is that \vec OM = \frac{1}{2}(a + b) and that \vec OP = \frac{1}{2}(b + c),

then you are, in fact, right (and the book is wrong). a, b and c are position vectors - which means they define the positions of points A, B and C respectively with respect to a common origin O. By convention, they *always* point outward from the origin O toward the terminal point. So a = \vec OA, etc.

OK just wanted to clear that up yeah in the book the have 1/2(b-a),1/2(b-c)... thanks for the quick reply! Keep it ℝeal!