Question

What is the volume of the parallelepiped determined by the vectors ⃗ = 〈1, 3, 0〉, ⃗⃗ = 〈2, −2, 0〉, and ⃗ = 〈2, 3, 5〉? A) 7 cubic units B) 15 cubic units C) 18 cubic units D) 30 cubic units

Answer 1

The volume of the parallelepiped determined by the given vectors is 40 cubic units.

Step-by-step explanation:

To find the volume of the parallelepiped determined by the given vectors, we can use the dot product and the cross product. First, calculate the cross product of the vectors A and B, then take the dot product of the resulting vector with C. The absolute value of the dot product will give us the volume of the parallelepiped.

Calculating the cross product of A and B: A x B = (1, 3, 0) x (2, -2, 0) = (0, 0, -8)

Taking the dot product of the resulting vector with C: (0, 0, -8) . (2, 3, 5) = 0 + 0 + (-40) = -40.

The volume of the parallelepiped is the absolute value of the dot product, so the answer is 40 cubic units.