# Worksheet: Equation of a Plane: Intercept and Parametric Forms

In this worksheet, we will practice finding the equation of a plane in different forms, such as intercept and parametric forms.

**Q1: **

Find the general equation of the plane , , .

- A
- B
- C
- D
- E

**Q2: **

Write, in intercept form, the equation of the plane .

- A
- B
- C
- D
- E

**Q3: **

What is the length of the segment of the -axis cut off by the plane ?

- A of a length unit
- B8 length units
- C32 length units
- D4 length units

**Q4: **

Find the general form of the equation of the plane which intersects the coordinate axes at the points , , and .

- A
- B
- C
- D

**Q5: **

Given that the plane intersects the coordinate axes , , and at the points , , and , respectively, find the area of .

- A
- B
- C
- D
- E

**Q6: **

Determine the general equation of the plane that intersects the negative -axis at a distance of 2 from the origin, intersects the positive -axis at a distance of 3 from the origin, and passes through the point .

- A
- B
- C
- D
- E

**Q7: **

Find the general equation of the plane that passes through the point and cuts off equal intercepts on the three coordinate axes.

- A
- B
- C
- D
- E

**Q8: **

Find the equation of the plane cutting the coordinate axes at , , and , given that the intersection point of the medians of is .

- A
- B
- C
- D
- E

**Q9: **

Find the equation of the plane whose -, -, and -intercepts are , 3, and , respectively.

- A
- B
- C
- D

**Q10: **

What is the length of the segment of the cut off by the plane ?

- A
- B
- C
- D
- E

**Q11: **

Choose the possible parametric equation of the plane .

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