Calculus and vectors-Help~David

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Rectangular prism is defined by vectors (2,0,0)(0,9,5) and (0,0,3). Find the volume.

I have done this so far, would anyone please verify this.

(2,0,0)(0,9,6)

(0-2, 9-0, 6-0)
=(-2,9,6)

(-2,9,6)(0,0,3)

=(2,-9,-3)

(2)(-9)(-3)=54 cm^3

Therefore volume is 54 cm^3

  • Calculus and vectors-Help~David -

    54 cm^3 is the correct answer

    I do it differently:
    if given 3 vectors a, b, and c
    volume of parallelepiped
    =| a . (b X c) |

    (2,0,0) X (0,0,3) = (0, -6, 0)

    volume = |(0,9,5) . (0,-6,0) |
    = |0-54+0| = 54

  • Calculus and vectors-Help~David -

    Thank you very much!

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