Question

Please, explain me: find the volume of the parallelepiped determined by the vectors a(1,1,-1), b(1,-1,1) and c(1,1,-1).

Answer 1

to me, a,b, c perpendicular each other. so the volume of the parallelepiped is |a|^3 =3sqr(3).
to me, too: the volume of that is a product scalars of a.(bxc) = 4
I confuse. Anyone help me, please

Answer 2

you have vector a the same as vector c. Is that a mistake?

also, a dot b is not zero, so a and b are not perpendicular

Answer 3

Yes, you are right, mis-typo, c(-1,1,1)

Answer 4

Yes, I got it. they are not perpendicular to each other. but if a (1,0,0) b(0,1,0) and c (0,0,1) is perpendicular to each other, right? so, the formula a.(bxc) =4 is the right one, right?

Answer 5

yes, the "scalar triple product" of 3 vectors in 3-space gives the volume of a parallelepiped

you can compute it by taking the determinant of the 3 x 3 matrix formed by the 3 vectors

the determinant of the identity matrix is 1, which matches the volume of a (1,0,0) b(0,1,0) and c (0,0,1)

Answer 6

for volume, you take the absolute value (in the case you get a negative number)
http://www.wolframalpha.com/input/?i=det+%28%281%2C1%2C-1%29%2C+%281%2C-1%2C1%29+%2C+%28-1%2C1%2C1%29%29+

Answer 7

I got it. thanks a looot. I don't know how to type the problem into the box of Worframalpha. I type exactly what the book is, but the reply is "do not understand ... something" . moreover, what i need is my mistake or misunderstanding the concept, not the result. That's why I am here. Any way, again, I appreciate your help

Answer 8

by the way, can I make another question here?

Answer 9

post it as a new question.

Answer 10

no, I have a solution for that already, I just want to make clear some points. no need to occupy the chance of the others for my "not important" question. .but if you don't have time , I am ok. I know I am too greed when wanting more ways when solving the problem. My bad. sorry

Answer 11

Just post your question, and if someone can answer it they will try.

Answer 12

I'm sorry, sometimes I feel embarrassed because of my "stupid" questions. Once, a guys yelled at me when I asked for expand (1 -x)^10 before take derivative. At that time, I just wanted to make sure that I would not miss something when using generating function to figure out the coefficient of x^15. After then, I just ask what is a really stuck problem.