# Worksheet: Equation of a Plane: Vector, Scalar, and General Forms

In this worksheet, we will practice finding the vector, scalar (standard or component), and general (Cartesian or normal) forms of the equation of a plane given the normal vector and a point on it.

**Q2: **

Which of the following planes contains the straight line ?

- A
- B
- C
- D
- E

**Q3: **

Find the vector form of the equation of the plane that has normal vector and contains the point .

- A
- B
- C
- D

**Q4: **

Find the direction cosines of the normal to the plane .

- A
- B
- C
- D

**Q5: **

In which of the following planes does the point lie?

- A
- B
- C
- D
- E

**Q6: **

Which of the following points lies in the plane ?

- A
- B
- C
- D

**Q7: **

Find the general equation of the plane which passes through the point and contains the -axis.

- A
- B
- C
- D
- E

**Q8: **

Find the equation of the plane .

- A
- B
- C
- D
- E

**Q9: **

Find the equation of the plane which is perpendicular to the vector and passes through the point .

- A
- B
- C
- D
- E

**Q10: **

A plane passes through and has normal . Give its equation in vector form.

- A
- B
- C
- D

**Q11: **

Which of the following does the equation represent in three-dimensional space?

- Aa plane containing the -axis
- Ba plane containing the -axis
- Ca straight line whose direction ratios are
- Da plane containing the -axis

**Q12: **

Determine the general form of the equation for a plane in which the two straight lines and lie.

- A
- B
- C
- D

**Q13: **

Determine the Cartesian equation of the straight line passing through the point that is perpendicular to the plane .

- A
- B
- C
- D

**Q14: **

To which of the following planes is the straight line perpendicular?

- A
- B
- C
- D

**Q15: **

Find the general equation of the plane which passes through the two points and , given that the distance from the -intercept to the origin is equal to the distance from the -intercept to the origin.

- A
- B
- C
- D

**Q17: **

Find the equation, in vector form, of the plane passing through the points , , and .

- A
- B
- C
- D

**Q18: **

Find the vector form of the equation of the plane containing the two straight lines and .

- A
- B
- C
- D

**Q19: **

Which of the following is the equation of a plane that bisects the line segment between the two points and ?

- A
- B
- C
- D

**Q20: **

Given that is parallel to the plane , where the coordinates of and are and , respectively, find the value of .

**Q21: **

Find the Cartesian equation of the plane , where and are parameters.

- A
- B
- C
- D
- E

**Q23: **

Find the general equation of the plane which contains the straight line and the point .

- A
- B
- C
- D
- E

**Q24: **

Find the general equation of the plane which passes through the two points and and is parallel to the vector .

- A
- B
- C
- D
- E

**Q25: **

Find the general equation of the plane passing through the point and perpendicular to the straight line passing through the two points and .

- A
- B
- C
- D
- E