# Worksheet: Intersection of Planes

In this worksheet, we will practice finding the point/line of intersection between planes given their equations.

**Q1: **

Find the point of intersection of the planes , , and .

- A
- B
- C
- D
- E

**Q2: **

Find the point of intersection of the planes , , and .

- A
- B
- C
- D
- E

**Q3: **

Find the point of intersection of the planes , , and .

- A
- B
- C
- D
- E

**Q4: **

Find the point of intersection of the planes , , and .

- A
- B
- C
- D
- E

**Q5: **

Find the point of intersection of the planes , , and .

- A
- B
- C
- D
- E

**Q6: **

Find the coordinates of the point of intersection of the straight line with the plane .

- A
- B
- C
- D
- E

**Q7: **

Straight line is parallel to plane , and from a point neither on the line nor in the plane are drawn rays , meeting in and . If , what is the ratio between and ?

- A
- B
- C
- D

**Q8: **

Find the point of intersection of the straight line and the plane .

- A
- B
- C
- D

**Q9: **

Determine whether the following sentence is true or false: In every plane, any two intersecting lines are perpendicular.

- Atrue
- Bfalse

**Q10: **

Find the point of intersection of the planes , , and .

- A
- B
- C
- D
- E

**Q11: **

Which of the following is the direction vector of the line of intersection between the two planes and ?

- A
- B
- C
- D
- E

**Q12: **

Find the parametric equations of the line of intersection between the two planes and .

- A, , and
- B, , and
- C, , and
- D, , and
- E, , and

**Q13: **

Consider three intersecting planes. The normals to each of the planes are coplanar. Are the lines of intersection parallel?

- ANo
- BYes

**Q14: **

Find the vector equation of the line of intersection between the two planes and .

- A
- B
- C
- D
- E

**Q15: **

Find the point of intersection of the line with the plane .

- A
- B
- C
- D
- E

**Q16: **

Find the vector equation of the line of intersection between the two planes and .

- A
- B
- C
- D
- E