# Worksheet: The Equation of a Plane in 3D in Different Forms

Q1:

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

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Q2:

Which of the following points lies in the plane ?

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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.

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Q4:

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

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Q5:

Write, in normal form, the equation of the plane containing the point and perpendicular to the vector .

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Q6:

Find the general equation of a plane that is parallel to the -axis.

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Q7:

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

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Q8:

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

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Q9:

Determine the general equation of the plane that contains the straight line and that is perpendicular to the plane .

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Q10:

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

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• D

Q11:

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

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• E

Q12:

Find the general equation of a plane that is parallel to the -axis.

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• 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 , , .

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Q15:

Find the general equation of the plane which passes through the point and is perpendicular to the two planes and .

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• E

Q16:

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

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• D

Q17:

Find the equation of the plane .

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• E

Q18:

Find the general equation of a plane that is parallel to the -axis.

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• B
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• 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.

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• B
• C
• D

Q23:

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

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• 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