A parallelepiped is defined by the following vectors |𝑎| = (2, 3, −1), |𝑏| = (−1, 0, 2),
and |𝑐| = (3, −1, 2). Find the volume of the parallelepiped.
1
Expert's answer
2021-05-12T05:04:23-0400
The volume is given by the formula ∣a⋅∣b×c∣∣. We can write b=−i^+2k^ and c=3i^−j^+2k^.b×c=i^(−2×−1)+j^(2×3−(−1)×2)+k^(−1×−1)=2i^+8j^+k^. Hence a⋅(b×c)=(2i^+3j^−k^)⋅(2i^+8j^+k^) = 2×(2)+(3)×8−(1×1)=27. Hence volume =∣27∣=27 in cube units.
Comments