Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

In this lesson, we will learn how to find the equation of a plane using the x-, y-, and z-intercepts.

Q1:

Given that the plane 2 π₯ + 6 π¦ + 2 π§ = 1 8 intersects the coordinate axes π₯ , π¦ , and π§ at the points π΄ , π΅ , and πΆ , respectively, find the area of β³ π΄ π΅ πΆ .

Q2:

Determine the general equation of the plane that intersects the negative π₯ -axis at a distance of 2 from the origin, intersects the positive π§ -axis at a distance of 3 from the origin, and passes through the point πΆ ( 9 , β 4 , β 4 ) .

Q3:

Determine the general equation of the plane that intersects the negative π₯ -axis at a distance of 5 from the origin, intersects the negative π§ -axis at a distance of 6 from the origin, and passes through the point πΆ ( β 6 , 1 , β 2 ) .

Q4:

Determine the general equation of the plane that intersects the positive π₯ -axis at a distance of 6 from the origin, intersects the negative π§ -axis at a distance of 2 from the origin, and passes through the point πΆ ( 4 , 4 , β 3 ) .

Q5:

Determine the general equation of the plane that intersects the negative π₯ -axis at a distance of 6 from the origin, intersects the negative π§ -axis at a distance of 2 from the origin, and passes through the point πΆ ( 6 , β 6 , β 9 ) .

Q6:

Determine the general equation of the plane that intersects the negative π₯ -axis at a distance of 4 from the origin, intersects the positive π§ -axis at a distance of 7 from the origin, and passes through the point πΆ ( 5 , β 1 , 7 ) .

Q7:

Find the general equation of the plane that is perpendicular to the plane β 6 π₯ + 3 π¦ + 4 π§ + 4 = 0 and cuts the π₯ - and π¦ -axes at ( 5 , 0 , 0 ) and ( 0 , 1 , 0 ) respectively.

Q8:

Find the general equation of the plane that is perpendicular to the plane β 8 π₯ β π¦ + 6 π§ β 8 = 0 and cuts the π₯ - and π¦ -axes at ( 1 , 0 , 0 ) and ( 0 , β 6 , 0 ) respectively.

Q9:

Find the general equation of the plane that is perpendicular to the plane 6 π₯ β 5 π¦ β 7 π§ + 4 = 0 and cuts the π₯ - and π¦ -axes at ( β 1 , 0 , 0 ) and ( 0 , β 1 , 0 ) respectively.

Q10:

Find the general equation of the plane that is perpendicular to the plane 3 π₯ + 4 π¦ β 2 π§ β 8 = 0 and cuts the π₯ - and π¦ -axes at ( β 1 , 0 , 0 ) and ( 0 , β 6 , 0 ) respectively.

Q11:

Find the general equation of the plane that is perpendicular to the plane 8 π₯ β 5 π¦ + 8 π§ + 5 = 0 and cuts the π₯ - and π¦ -axes at ( β 4 , 0 , 0 ) and ( 0 , β 3 , 0 ) respectively.

Q12:

Find the general equation of the plane that passes through the point ( 8 , β 9 , β 9 ) and cuts off equal intercepts on the three coordinate axes.

Q13:

Find the general equation of the plane that passes through the point ( β 1 , 7 , 6 ) and cuts off equal intercepts on the three coordinate axes.

Q14:

Find the general equation of the plane that passes through the point ( β 5 , β 5 , 4 ) and cuts off equal intercepts on the three coordinate axes.

Q15:

Find the equation of the plane cutting the coordinate axes at π΄ , π΅ , and πΆ , given that the intersection point of the medians of β³ π΄ π΅ πΆ is ( π , π , π ) .

Donβt have an account? Sign Up