Show that the line \( \vec{r}=(4 \hat{i}-7 \hat{k})+\lambda(4 \hat{...

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Show that the line \( \vec{r}=(4 \hat{i}-7 \hat{k})+\lambda(4 \hat{i}-2 \hat{j}+3 \hat{k}) \) is parallel to the plane
\( \mathrm{P} \) \( \vec{r} \cdot(5 \hat{i}+4 \hat{j}-4 \hat{k})=7 \)

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