## Related questions with answers

Question

Determine whether the following statements are true and give an explanation or counterexample.

$| \mathbf { u } \times \mathbf { v } |$ is less than both $|u|$ and $|v|$.

Solution

VerifiedAnswered 9 months ago

Answered 9 months ago

Step 1

1 of 2Not true

Suppose $\mathbf u$ and $\mathbf v$ are orthogonal $\ \Rightarrow \ \sin \angle (\mathbf u, \mathbf v)=1$

Let $|\mathbf u|=1, |\mathbf v|=2$. Then

$|\mathbf u \times \mathbf v|=|\mathbf u| |\mathbf v|\sin \angle (\mathbf u, \mathbf v)=1\cdot 2\cdot 1=2$

So,

$|\mathbf u \times \mathbf v|>|\mathbf u|$

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