(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove [tex]\mathbf{PQ}\cdot \mathbf v=\int_a^b\frac{\textup d\gamma}{\textup d t}(t)\cdot\mathbf v\textup d t[/tex]

where [tex] \mathbf P=\gamma(a)[/tex] and [tex]\mathbf Q=\gamma(b)[/tex]

3. The attempt at a solution

I get

[tex]

\int_a^b\frac{\textup d\gamma}{\textup d t}(t)\cdot\mathbf v\textup d t=v_x\int_a^b{\frac{\textup d\gamma_x}{\textup d t}\textup d t}+v_y\int_a^b{\frac{\textup d\gamma_y}{\textup d t}\textup d t}+v_z\int_a^b{\frac{\textup d\gamma_z}{\textup d t}\textup d t}\\

=v_x(\gamma_x(b)-\gamma_x(a))+v_y(\gamma_y(b)-\gamma_y(a))+v_y(\gamma_y(b)-\gamma_y(a))\\

=\mathbf v\cdot(\mathbf{Q-P})[/tex]

I'm not sure how to turn this into what is given. I'm not even sure I know what the left hand side of the given identity means. Is it the same thing as

[tex]\mathbf{P}(\mathbf Q}\cdot \mathbf v)[/tex]

Any help would be appreciated. Thanks in advance :)

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# Homework Help: Vector Problem

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