JEE Main & Advanced
Mathematics
Three Dimensional Geometry
Question Bank
Critical Thinking
question_answer
If three mutually perpendicular lines have direction cosines \[({{l}_{1}},{{m}_{1}},{{n}_{1}}),({{l}_{2}},{{m}_{2}},{{n}_{2}})\]and \[({{l}_{3}},{{m}_{3}},{{n}_{3}})\], then the line having direction cosines \[{{l}_{1}}+{{l}_{2}}+{{l}_{3}}\], \[{{m}_{1}}+\,\,{{m}_{2}}+\,\,{{m}_{3}}\]and \[{{n}_{1}}+{{n}_{2}}+{{n}_{3}}\] make an angle of ..... with each other
A)\[0{}^\circ \]
B)\[30{}^\circ \]
C)\[60{}^\circ \]
D)\[90{}^\circ \]
Correct Answer:
A
Solution :
Lines are mutually perpendicular
\ \[{{l}_{1}}{{l}_{2}}+{{m}_{1}}{{m}_{2}}+{{n}_{1}}{{n}_{2}}=0,\,\,\,{{l}_{2}}{{l}_{3}}+{{m}_{2}}{{m}_{3}}+{{n}_{2}}{{n}_{3}}=0\] and \[{{l}_{1}}{{l}_{3}}+{{m}_{1}}{{m}_{3}}+{{n}_{1}}{{n}_{3}}=0\]