Start Practicing
Worksheet: The Equation of a Plane in 3D in Different Forms
Q1:
Find the Cartesian equation of the plane , where and are parameters.
- A
- B
- C
- D
- E
Q2:
Which of the following points lies in the plane ?
- A
- B
- C
- D
Q3:
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
Q4:
Find the equation, in vector form, of the plane passing through the points , , and .
- A
- B
- C
- D
Q5:
Write, in normal form, the equation of the plane containing the point and perpendicular to the vector .
- A
- B
- C
- D
- E
Q6:
Find the general equation of a plane that is parallel to the -axis.
- A
- B
- C
- D
- E
Q7:
Find the vector form of the equation of the plane containing the two straight lines and .
- A
- B
- C
- D
Q8:
Determine the Cartesian equation of the straight line passing through the point that is perpendicular to the plane .
- A
- B
- C
- D
Q9:
Determine the general equation of the plane that contains the straight line and that is perpendicular to the plane .
- A
- B
- C
- D
- E
Q10:
Which of the following is the equation of a plane that bisects the line segment between the two points and ?
- A
- B
- C
- D
Q11:
Find the equation of the plane which is perpendicular to the vector and passes through the point .
- A
- B
- C
- D
- E
Q12:
Find the general equation of a plane that is parallel to the -axis.
- A
- B
- C
- D
- E
Q13:
Given that is parallel to the plane , where the coordinates of and are and , respectively, find the value of .
Q14:
Find the general equation of the plane , , .
- A
- B
- C
- D
- E
Q15:
Find the general equation of the plane which passes through the point and is perpendicular to the two planes and .
- A
- B
- C
- D
- E
Q16:
A plane passes through and has normal . Give its equation in vector form.
- A
- B
- C
- D
Q17:
Find the equation of the plane .
- A
- B
- C
- D
- E
Q18:
Find the general equation of a plane that is parallel to the -axis.
- A
- B
- C
- D
- E
Q19:
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
Q20:
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
Q21:
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
Q22:
Determine the general form of the equation for a plane in which the two straight lines and lie.
- A
- B
- C
- D
Q23:
Write, in intercept form, the equation of the plane .
- A
- B
- C
- D
- E
Q24:
In which of the following planes does the point lie?
- A
- B
- C
- D
- E
Q25:
To which of the following planes is the straight line perpendicular?
- A
- B
- C
- D