If \( \mathbf{r}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\lambda(2 \hat{\...

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If \( \mathbf{r}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\lambda(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+4 \hat{\mathbf{k}}) \) and \( \mathbf{r} \cdot(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})=3 \) are the equations of a line and a plane respectively, then which
\( \mathrm{P} \) of the following is incorrect?

W
(a) line is perpendicular to the plane
(b) line lies in the plane
(c) line is parallel to the plane but does not lie in the plane
(d) line cuts the plane obliquely
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