# 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.

Q1:

Write, in normal form, the equation of the plane , and .

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Q2:

Which of the following planes contains the straight line ?

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Q3:

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

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Q4:

Find the direction cosines of the normal to the plane .

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Q5:

In which of the following planes does the point lie?

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Q6:

Which of the following points lies in the plane ?

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Q7:

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

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Q8:

Find the equation of the plane .

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Q9:

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

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Q10:

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

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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.

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Q13:

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

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Q14:

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

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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.

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Q16:

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

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Q17:

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

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Q18:

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

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Q19:

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

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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.

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Q22:

Write, in normal form, the equation of the plane containing , , and .

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Q23:

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

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Q24:

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

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Q25:

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

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