The volume of the parallelepiped determined by the vectors a=(1,2,3), b=(-1, 1, 2) and c=(2, 1, 4) Question 12Answera.18 cubic unitsb.9 cubic unitsc.15/2 cubic unitsd.9 sq. units
Question
The volume of the parallelepiped determined by the vectors a=(1,2,3), b=(-1, 1, 2) and c=(2, 1, 4) Question 12Answera.18 cubic unitsb.9 cubic unitsc.15/2 cubic unitsd.9 sq. units
Solution
The volume of a parallelepiped determined by three vectors a, b, and c can be found using the scalar triple product, which is the absolute value of the dot product of one of the vectors with the cross product of the other two vectors.
The formula is: V = |a . (b x c)|
First, we need to find the cross product of vectors b and c.
b x c = ((14 - 21), (-14 - 22), (-11 - 12)) = (2, -8, -3)
Then, we find the dot product of vector a and the result of the cross product of vectors b and c.
a . (b x c) = (12 + 2(-8) + 3*(-3)) = 2 - 16 - 9 = -23
The volume of the parallelepiped is the absolute value of this result.
V = |-23| = 23 cubic units
However, this answer is not listed in the options you provided. Please check the vectors or the answer options.
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