The position vector of the points \( A, B, C \) and \( D \) are \( 3 \hat{i}-2 \hat{j}-\hat{k}, ...

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The position vector of the points \( A, B, C \) and \( D \) are \( 3 \hat{i}-2 \hat{j}-\hat{k}, 2 \hat{i}+3 \hat{j}-4 \hat{k} \),
\( \mathrm{P} \) \( -\hat{i}+\hat{j}+2 \hat{k} \) and \( 4 \hat{i}+5 \hat{j}+\lambda \hat{k} \). It is known that these points are coplanar, then \( \lambda \)

W is equal to:
(A) \( -\frac{146}{17} \)
(B) \( -\frac{137}{17} \)
(C) \( -\frac{154}{17} \)
(D) None of these
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