question_answer

Let \[{{L}_{1}}:\overrightarrow{r}=\hat{i}-\hat{j}-10\hat{k}+\lambda (2\hat{i}-3\hat{j}+8\hat{k})\] and \[{{L}_{2}}:\overrightarrow{r}=4\hat{i}-3\hat{j}-\hat{k}+\mu (\hat{i}-4\hat{j}+7\hat{k})\] represent two lines in R3, then which one of the following is incorrect?

A)  \[{{L}_{1}}\] is parallel to the vector \[4\hat{i}-6\hat{j}+16\hat{k}.\]

B)   \[{{L}_{2}}\]is parallel to the vector \[-\hat{i}+4\hat{j}-7\hat{k}.\].

C)  \[{{L}_{1}}\] and \[{{L}_{2}}\] are coplanar.

D)  Angle between the lines \[{{L}_{1}}\] and \[{{L}_{2}}\] is \[{{\cos }^{-1}}\left( \frac{70}{11\sqrt{7}} \right)\].