# Worksheet: Equations of Parallel and Perpendicular Lines in Space

In this worksheet, we will practice finding the equation of a straight line that is parallel or perpendicular to another one in space and finding the intersection point between two lines.

**Q1: **

The straight line that passes through the point is perpendicular to the vector . Find the Cartesian equation of the line.

- A
- B
- C
- D

**Q2: **

What is the equation of the line parallel to line and passing through ?

- A
- B
- C
- D

**Q3: **

Find the Cartesian form of the equation of the straight line passing through the origin and the intersection point of the two straight lines and , .

- A
- B
- C
- D

**Q4: **

Find the vector form of the equation of the straight line passing throught the point and parallel to the straight line passing through the two points and .

- A
- B
- C
- D

**Q5: **

Find the vector form of the equation of the straight line passing through the point and the intersection point of the two straight lines and .

- A
- B
- C
- D

**Q6: **

Determine the vector form of the equation of the straight line passing through the point and parallel to the vector .

- A
- B
- C
- D

**Q7: **

Given that is perpendicular to , what is ?

**Q8: **

Given that the vector is parallel to the line , find .

**Q9: **

Find the parametric equations of the straight line that passes through the point and that is parallel to the bisector of the second quadrant of the plane .

- A, ,
- B, ,
- C, ,
- D, ,

**Q11: **

Given that the lines and are perpendicular, what is ?

**Q12: **

Find the equation of the line through the origin that intersects the line orthogonally.

- A
- B
- C
- D

**Q13: **

For what value of do the lines and intersect?

**Q14: **

For what values of is the line parallel to the line ?