What is the volume of a parallelepiped whose coterminous edges are a = 2î − 3ĵ + 4k̂, b = î + 2ĵ − k̂, and c = 3î − ĵ + 2k̂? A. −7 B. 7 C. 14 D. 0 Answer: B) 7 Explanation: Volume V = |[a b c]|. The determinant = 2(4 − 1) − (−3)(2 + 3) + 4(−1 − 6) = 2(3) + 3(5) + 4(−7) = 6 + 15 − 28 = −7. Since volume is positive, V = |-7| = 7 cubic units.

imo class 12 vector algebra

What is the volume of a parallelepiped whose coterminous edges are a = 2î − 3ĵ + 4k̂, b = î + 2ĵ − k̂, and c = 3î − ĵ + 2k̂?

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What is the volume of a parallelepiped whose coterminous edges are a = 2î − 3ĵ + 4k̂, b = î + 2ĵ − k̂, and c = 3î − ĵ + 2k̂?

A. −7
B. 7
C. 14
D. 0

Answer: B) 7

Explanation: Volume V = |[a b c]|. The determinant = 2(4 − 1) − (−3)(2 + 3) + 4(−1 − 6) = 2(3) + 3(5) + 4(−7) = 6 + 15 − 28 = −7. Since volume is positive, V = |-7| = 7 cubic units.

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