Question:
Show that the line $\vec{r}-(2 \hat{i}-2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}+4 \hat{k})$ is parallel to the plane $\vec{r} \cdot(\hat{i}+5 \hat{j}+\hat{k})-7$.
Solution:
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