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Kenzie
Kenzie asked in Science & MathematicsMathematics · 6 years ago

Find the volume of the parallelepiped determined by the vectors a, b, and c.?

a = 3i + 4j - 4k

b = i - j

c = 2i + 3k

I thought the equation was |a dot (b X c)|.

My work:

<3,4,-4> dot (-3-0)i - (3-0)j + (0-2)k

<3,4,-4> dot -3i -3j -2k

-9 -12 +8

=13

However, I am getting the wrong answer. Can somebody please figure out what I am doing wrong? Thanks.

2 Answers

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  • Rita the dog
    Lv 7
    6 years ago

    b x c = -3i - 3j + 2k

    a ⋅ b x c = (3i + 4j - 4k) ⋅ ( -3i - 3j + 2k) = (3)(-3) + (4)(-3) + (-4)(2) = -29

    So, taking absolute value, the volume of the parallelepiped is 29.

  • Anonymous
    6 years ago

    It's in the cross product:

    b X c = <-3, -3, 2>

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