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Bit of quick help please.

Need to know this for a test tomorrow.

Use the vector product to nd the area of the triangle with vertices A(1 1 2), B(0 4 3),
C = (2 1 1).


Please explian, i keep getting route 2?
u = a - b = (1, -3, -1)
v = c - b = (2, -3, -2)

Unparseable latex formula:

\mathbf{u} \times\mathbf{v} = \det\,\left(\begin{matrix}[br]\mathbf{i} & \mathbf{j} & \mathbf{k} \\[br]1 & -3 & -1\\[br]2 & -3 & -2[br]\end{matrix}\right)



i(6-3) - j(-2+2) + k(-3+6) = 3i - 3k

9+0+9=18=32\sqrt{9 + 0 + 9} = \sqrt{18} = 3\sqrt{2}
A Large Town In France
u = a - b = (1, -3, -1)
v = c - b = (2, -3, -2)

Unparseable latex formula:

\mathbf{u} \times\mathbf{v} = \left(\begin{matrix}[br]\mathbf{i} & \mathbf{j} & \mathbf{k} \\[br]1 & -3 & -1\\[br]2 & -3 & -2[br]\end{matrix}\right)



i(6-3) + j(-2+2) + k(-3+6) = 3i - 3k

9+0+9=18=32\sqrt{9 + 0 + 9} = \sqrt{18} = 3\sqrt{2}


You mean 3/sqrt(2), since he's asking for the area of the triangle rather than the parallelogram :p:

:o: Sorry for being pedantic, but j is usually associated with a "-". I know it's 0 and doesn't make a difference in this case.....
ukdragon37
You mean 3/sqrt(2), since he's asking for the area of the triangle rather than the parallelogram :p:


Oops, missed that step out when reformatting. (Making it completely explicit for the benefit of the OP: I forgot to divide by two.)

:o: Sorry for being pedantic, but j is usually associated with a "-". I know it's 0 and doesn't make a difference in this case.....


EDIT: Ah, whoops, misunderstood. You're right, thanks. Apparently maths and late hours don't mix with me. :o:
A Large Town In France

Hm, I'm not sure if I'll change that, since it's purely stylistic. I find the 0s ugly. But good to know, thanks. :smile:


I usually write -j(...) even if it's 0, just remind myself that it's +i and +k but -j. I'm just paranoid about everything though :o:
ukdragon37
I usually write -j(...) even if it's 0, just remind myself that it's +i and +k but -j. I'm just paranoid about everything though :o:


See edit. :smile:
Can I just ask...is this advanced higher maths? :p:
FuturePilot
Can I just ask...is this advanced higher maths? :p:


Funnily enough, yes it is :p:
ukdragon37
Funnily enough, yes it is :p:


Phew! :p:
I was wondering because I didn't recognise it!

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