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 \[{{\cos }^{-1}}\left( \frac{70}{11\sqrt{7}} \right)\].
Correct Answer: D
Solution :
\[{{L}_{1}}\] and \[{{L}_{2}}\] are intersecting lines. The position vector of their point of intersection is \[5\hat{i}-7\hat{j}\,+6\hat{k}\] (For \[\lambda =2\] or\[\mu =1\]). Also, angle between \[{{L}_{1}}\] and \[{{L}_{2}}\,=\frac{70}{\,11\sqrt{42}}\]You need to login to perform this action.
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