In this worksheet, we will practice finding the equation of a plane in different forms like the general, vector, and parametric forms.

**Q1: **

Find the general equation of the plane , , .

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**Q2: **

In which of the following planes does the point lie?

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**Q3: **

Which of the following points lies in the plane ?

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**Q4: **

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

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**Q5: **

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

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**Q6: **

Find the equation of the plane .

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**Q7: **

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

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**Q8: **

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

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**Q9: **

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

**Q10: **

Determine the general form of the equation for a plane in which the two straight lines and lie.

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**Q11: **

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

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**Q12: **

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

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**Q13: **

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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**Q14: **

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

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**Q15: **

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

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**Q16: **

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

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**Q17: **

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

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**Q18: **

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

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**Q19: **

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

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**Q20: **

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

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**Q21: **

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

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**Q22: **

Given that is parallel to the plane , where the coordinates of and are and , respectively, find the value of .

**Q23: **

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

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**Q24: **

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

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**Q25: **

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

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