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# Find the volume of the parallelepiped determined by vectors a,b,c a = i + j - k, b = i - j + k, c = -i+j+k?

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- UniversalistLv 76 years agoFavorite Answer
You just need to calculate the scalar triple product a . (b x c) which is equal to the absolute value of the 3x3 determinant

| 1 1 -1 |

| 1 -1 1 |

| -1 1 1 |

Expanding via the first row, I calculate it to be abs(1 x (-1 - 1) - 1 x (1 + 1) - 1 x (1 - 1)) = abs(-4) = 4 cubic units.

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