In this worksheet, we will practice determining the relationship between a straight line and a plane.

**Q1: **

The equation of a straight line is and the equaton of a plane is . Which of the following describes the relationship between and ?

- A
- B
- CThey meet at a point but are not perpendicular.
- D

**Q2: **

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

- A
- B
- C
- D
- E

**Q3: **

Which of the following makes the straight line lie on the plane ?

- A
- B
- C
- D and
- E

**Q4: **

In the figure, lies in the plane , and is perpendicular to . Given that and , find the length of .

**Q5: **

is a triangle with and . is drawn perpendicular to the plane of , and the perpendicular to from drawn to meet it at . If , determine the length of and the angle between and the plane of .

- A19.92,
- B30.43,
- C19.92,
- D11.5,
- E11.5,

**Q6: **

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

**Q7: **

What is ?

- A
- B
- C
- D

**Q8: **

Triangle is right angled at , and is orthogonal to the plane . A perpendicular is drawn from on . The area of is 1 134, , and . Let be the angle between and the plane . Find to the nearest thousandth.

**Q9: **

In which of the following cases is the straight line parallel to the plane ?

- A
- B
- C
- D
- E

**Q10: **

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

- A
- B
- C
- D
- E

**Q11: **

Find, to the nearest second, the measure of the smaller angle between the straight line and the plane .

- A
- B
- C
- D

**Q12: **

Which of the following scenarios would make plane ?

- A The distance from to is not the same as the distance from to .
- B and lie on two different sides of .
- C .
- D .

**Q13: **

The given figure shows a pyramid placed on plane . Find the intersection of the plane through points and plane ?

- A
- B
- C
- D
- E

**Q14: **

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

- A false
- B true

**Q15: **

Express the normal form of the plane containing the lines , , and , , .

- A
- B
- C
- D
- E

**Q16: **

Let be the surface you get by removing the point from the sphere with centre and radius 1, and let be an arbitrary point on . The line through and intersects the -plane at , as shown in the figure. Find the coordinates of this point in terms of , , and .

- A