Answer :
Final answer:
The lines formed by the intersection of ( l_1 ) and ( l_2 ) can be:
2) A line perpendicular to ( l_1 )4)
A line perpendicular to ( l_2 )
Therefore, options 2) and 4) are correct.
Explanation:
When two lines( l_1 ) and ( l_2 ) intersect, the intersection forms angles between them.
These angles could be of various measures depending on how( l_1 ) and ( l_2 ) are oriented in space.
Let's consider the options:
1) A line parallel to( l_1 ): If a line is parallel to ( l_1 ), it would not intersect with ( l_1 ), so it cannot be formed by the intersection of ( l_1 ) and ( l_2 ).
2) A line perpendicular to ( l_1 ): When two lines intersect and form right angles (90 degrees) at their intersection point, they are said to be perpendicular to each other.
Therefore, a line perpendicular to ( l_1 ) can indeed be formed by the intersection of ( l_1 ) and ( l_2 ).
3) A line parallel to ( l_2 ): Similar to option 1, if a line is parallel to ( l_2 ), it would not intersect with ( l_2 ), so it cannot be formed by the intersection of ( l_1 ) and ( l_2 ).
4) A line perpendicular to ( l_2 ): Similar to option 2, a line perpendicular to ( l_2 ) can be formed by the intersection of ( l_1 ) and ( l_2 ).
Therefore, options 2) and 4) are correct.
