Calculate the volume of the area enclosed by the following vectors.
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Hello!
I'm certainly a beginner when it comes to MatLAB, but I can find my way around eventually; except with this problem. I'm given the following to find, with the givens:
Use the determinate, or norm, to calculate the volume of the area enclosed by the following vectors.
a = 2*i+1*j+1*k
b= 2*i+-2*j+6*k
c=0*i+0*j+9*k
This is all that's given to me. When I enter this into MatLAB, it returns the error message, "??? Undefined function or variable 'k'." When I first looked at this problem, my first thought was, what are "i," "j," and "k." But I came to the conclusion that "i," and "j," are just the imaginary units, but I still have no idea what "k" is. Any help is appreciated!
Thanks!
4 Comments
Sven
on 12 Feb 2013
You need to understand in your homework what i, j, and k actually mean. They are not variables for you to plug into an equation. What if your question stated:
a = 2*x+1*y+1*z
What do x, y and z represent?
If you can answer that question, you'll be able to do this homework without any problems.
Accepted Answer
Youssef Khmou
on 13 Feb 2013
hi, like other users said , you need to understand that i,j,and k represent the Unitary vectors for Orthonormal basis -> -> -> ( i, j, k) with coordinates : i(1,0,0), j(0,1,0) and k(0,0,1),
You can create these vectors right? then you can create also the vectors a,b,c , so what type of product that gives a volume ?
THINK OF : Mixed product, Determinant, Base , columns .
2 Comments
Youssef Khmou
on 13 Feb 2013
ok good, we can explain this Geometrically :
you take the cube formed by (i,j,k) as reference , obviously the volume is 1 . so negative value is an issue of Orientation :
If you make a "parallelepiped" from random 3d vectors , and it takes at least one symmetry to go back to the unitary volume built by the unit vectors then the Sign is < 0.
Example :
a volume obtained from a=-5x-7y-6z, b=-11x-8y-41z, c=-14x-77y-36z
The sign is positive V=29048, because you only need deformation to get a unitary volume , but no symmetry, is it clear ?
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