Question

Hi can someone help me calculate the volume of a parallelepiped constructed with the following vectors:
a = i + j - k
b = i - j + k
c = -i + j + k
Thanks!

Answer 1

Volume = \( (\vec{a} \times \vec{b} ) . \vec{c} \)

Answer 2

take the cross product of any two vectors, and dot wid the other vector

Answer 3

The thing is that I get a negative answer... which is -4 .. the answer is 4 .. Do o need to take the absolute value of my asnwer ?

Answer 4

yes take absolute value,
Volume/length/area are always positive

Answer 5

Perfect, I was just confused to wether i was doing something wrong given the negative sign.. Thanks!

Answer 6

negative sign can be easily fixed by choosing the vectors in a different order. so yes nthng to wry :)

Answer 7

Volume = \((\vec{b} \times \vec{a} ) . \vec{c}\)

Answer 8

u wil get positive answer now :)