Now solved: Proof In Exercises 6774, prove the property. In each case, assume and are
Chapter 12, Problem 73(choose chapter or problem)
Proof In Exercises 67-74, prove the property. In each case, assume r, u, and v are differentiable vector-valued functions of t in space, w is a differentiable real-valued function of t, and c is a scalar.
\(\begin{array}{c}\frac{d}{d t}\{\mathbf{r}(t) \cdot[\mathbf{u}(t) \times\mathbf{v}(t)]\}=\mathbf{r}^{\prime}(t) \cdot[\mathbf{u}(t) \times\mathbf{v}(t)]+ \\\mathbf{r}(t) \cdot\left[\mathbf{u}^{\prime}(t) \times\mathbf{v}(t)\right]+\mathbf{r}(t) \cdot\left[\mathbf{u}(t) \times\mathbf{v}^{\prime}(t)\right]\end{array}\)
Text Transcription:
d/dt {r(t) times [u(t) times v(t)]} = r’(t) times [u(t) times v(t)] + r(t) times [u’(t) times v(t)] + r(t) times [u(t) times v’(t)]
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