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The point \( \vec{A}(3,4,7), \vec{B}(4,5,9) \) and \( \vec{C}(1,2,-1) \) are
P three vertices of a parallelogram \( A B C D \), then:

W
(1) Vector equation of line \( A B \) is
\[
\vec{r}=4 \hat{i}+5 \hat{j}+9 \hat{k}+\lambda(\hat{i}+\hat{j}+2 \hat{k})
\]
(2) Cartesian equation of line \( B C \) is
\[
\frac{x-4}{3}=\frac{y-5}{3}=\frac{z-9}{10}
\]
(3) Coordinates of \( D \) are \( (0,1,-3) \)
(4) \( A B C D \) is rectangle
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