High School

Consider the lines \( l_1 \) and \( l_2 \). Which of the following lines can be formed by the intersection of \( l_1 \) and \( l_2 \)?

1. A line parallel to \( l_1 \)
2. A line perpendicular to \( l_1 \)
3. A line parallel to \( l_2 \)
4. A line perpendicular to \( l_2 \)

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.