The volume of the parallelepiped whose adjacent sides are the vectors and $\mathbf { u } = 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }$ is

A) $\sqrt { 6897 }$
B) $\sqrt { 6993 }$
C)62
D)70
E)82

Question

The volume of the parallelepiped whose adjacent sides are the vectors and $\mathbf { u } = 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }$ is

A) $\sqrt { 6897 }$
B) $\sqrt { 6993 }$
C)62
D)70
E)82

Quizplus · Accepted Answer

The volume of a parallelepiped formed by three vectors can be found using the scalar triple product of those vectors. In this case, since only one vector $\mathbf{u} = 2\mathbf{i} + \mathbf{j} - 2\mathbf{k}$ is provided and the question seems to be missing the other two vectors, we cannot directly compute the volume. However, given the options and assuming a mistake in the question's phrasing, if we were to calculate the volume of a parallelepiped with identical or similarly defined vectors, we would use the determinant of a matrix formed by the components of these vectors. Without the other vectors, we cannot proceed with a standard calculation. The correct answer, therefore, is based on the assumption that there's an error in the question. However, since "C" is marked as correct, it suggests there might be an intended or expected method to interpret or correct the question that isn't directly addressed in the provided information.

The Volume of the Parallelepiped Whose Adjacent Sides Are the Vectors