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Multivariable Calculus

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Statements on Cross Products

MVCALC-5DNBCJ

Which of the following statements is always TRUE?

A

If ${\bf v}$ and ${\bf w}$ are two unit vectors and the angle $\alpha$ that they make increases, then the length of ${\bf v} \times {\bf w}$ also increases.

B

If ${\bf v}$ and ${\bf w}$ are two unit vectors and the angle $\alpha$ that they make changes, then the length of ${\bf v} \times {\bf w}$ also changes.

C

If ${\bf u}$, ${\bf v}$ and ${\bf w}$ are all nonzero vectors, and ${\bf u} \times {\bf w} = {\bf u} \times {\bf v},$ then ${\bf w} = {\bf v}$.

D

Let ${\bf v}$ and ${\bf w}$ be nonparallel. The vector ${\bf u} \times ({\bf v} \times {\bf w})$ is coplanar with the vectors ${\bf v}$ and ${\bf w}$.

E

If ${\bf u}$ and ${\bf v}$ are nonzero vectors, then $||{\bf u} \times {\bf v} || \neq {\bf u} \cdot {\bf v}.$