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 negativeΒ -axis at a distance of 2 from the origin, intersects the positiveΒ -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, ,