please help me solve this problem


Given that a=2i-j-k,b=2i+j-2k and c= -i+j-k are the position vectors of the points A, B, and C respectively, calculate the area of triangle ABC.

Find vectors AB and AC, say. Take their cross product. Take half of the magnitude of the cross product. Viola! the answer.

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Thanks for the help although i am still a bit confused. Would you mind walking me through the problem.

I really appreciate all the help THANK YOU!!!!

Well, I'll add a bit more but you need to say where you're confused ....

To find vector AB, note that AB = AO + OB = -OA + OB.
OA is the position of the point A: OA = a = 2i - j - k.
OB is the position of the point B: OB = b = 2i + j - 2k.

Therefore AB = -OA + OB = -(2i - j - k) + 2i + j - 2k = 2j - k.

In a similar way, get AC.

Now ..... do you know how to find the cross-product of two vectors?

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I really am still confused because i have not learned this in my class. I am taking Trigonometry/ Precalculus and my teacher gave us a packet to keep busy because we took our final already, although this packet is counted as homework.

i dont know if you could like i said walk me through the problem, as i have others like it. i would appreciate at least having this as an example.

thank you!!!!!!!!!

you've helped me a ton... lol...

i really do appreciate it.

hey you are truly a nice person for taking the time to help people with their math problems. LOL truly you are......

Well, if you're given a question that has vectors in it, you must have been taught something about vectors. So the natural thing to ask is: What do you know about vectors?

In the meantime, here's an alternative method:

You can use the position vectors to label the coordinates of each vertex of the triangle. If you know the coordinates of the vertices, you can calculate the distance between the vertices (using the usual formula for the distance between two points). In other words, you can calculate the length of each side of the triangle.

So the question boils down to: How do you find the area of a triangle when you know the lengths of each side?

Read post #6 of this thread to see how you might answer that question.

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so we use Herons formula

That would be the best way I think. Even if you've never formally learned it, it's a pretty simple formula. (But the proof of it, that's another matter).

But note that it can be done using the cosine rule and then the usual formula for area of triangle (as mentioned in the thread I drew your attention to).

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that sounds good i will try to see if i can find the answer