# Worksheet: Equation of a Plane in Space

In this worksheet, we will practice finding the equation of a plane using the x-, y-, and z-intercepts.

**Q1: **

Determine the general equation of the plane that intersects the negative -axis at a distance of 2 from the origin, intersects the positive -axis at a distance of 3 from the origin, and passes through the point .

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**Q2: **

Find the general equation of the plane that is perpendicular to the plane and cuts the - and -axes at and respectively.

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**Q3: **

Find the general equation of the plane that passes through the point and cuts off equal intercepts on the three coordinate axes.

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**Q4: **

Given that the plane intersects the coordinate axes , , and at the points , , and , respectively, find the area of .

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**Q5: **

Find the equation of the plane cutting the coordinate axes at , , and , given that the intersection point of the medians of is .

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**Q6: **

Find the equation of the plane whose -, -, and -intercepts are , 3, and , respectively.

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**Q7: **

Determine the general equation of the plane that intersects the negative -axis at a distance of 5 from the origin, intersects the negative -axis at a distance of 6 from the origin, and passes through the point .

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**Q8: **

Determine the general equation of the plane that intersects the positive -axis at a distance of 6 from the origin, intersects the negative -axis at a distance of 2 from the origin, and passes through the point .

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**Q9: **

Determine the general equation of the plane that intersects the negative -axis at a distance of 6 from the origin, intersects the negative -axis at a distance of 2 from the origin, and passes through the point .

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**Q10: **

Determine the general equation of the plane that intersects the negative -axis at a distance of 4 from the origin, intersects the positive -axis at a distance of 7 from the origin, and passes through the point .

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**Q11: **

Find the general equation of the plane that is perpendicular to the plane and cuts the - and -axes at and respectively.

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**Q12: **

Find the general equation of the plane that is perpendicular to the plane and cuts the - and -axes at and respectively.

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**Q13: **

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**Q14: **

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**Q15: **

Find the general equation of the plane that passes through the point and cuts off equal intercepts on the three coordinate axes.

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