# Equation of a Plane : General Form

## Trending Questions

**Q.**Let the equation of the pair of lines, y=px and y=qx, can be written as (y−px)(y−qx)=0. Then the equation of the pair of the angle bisectors of the lines x2−4xy−5y2=0 is

- x2−3xy+y2=0
- x2+3xy−y2=0
- x2−3xy−y2=0
- x2+4xy−y2=0

**Q.**A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is y2z2+z2x2+x2y2=kx2y2z2, where k is equal to

- 9p2
- 9p2
- 16p2
- 7p2

**Q.**A piece of cheese is located at (12, 10) in a coordinate plane. A mouse is at (4, –2) and is running up the line y = –5x + 18. At the point (a, b), the mouse starts getting farther from the cheese rather than closer to it. The value of (a + b) is

- 6
- 10
- 18
- 14

**Q.**If a plane passes through the point (1, 1, 1) and is perpendicular to the line x−13=y−10=z−14 then its perpendicular distance from the origin is

- 1
- 34
- 43
- 75

**Q.**If the general equation of plane is given by ax + by + cz = d then a, b, c are the

- normal
- tangent
- direction cosines
- direction ratios

**Q.**Consider the three planes

P1:3x+15y+21z=9

P2:x−3y−z=5, and

P3:2x+10y+14z=5

Then, which one of the following is true ?

- P1 and P3 are parallel.
- P2 and P3 are parallel.
- P1, P2 and P3 all are parallel.
- P1 and P2 are parallel.

**Q.**

The equation of the plane passing through the points (1, -1, 2) and (2, -2 2) and which is perpendicular to the plane 6x -2y +2z =9 is

x+y−2z+4=0

x−y−2z=4

x−2y+z−4=0

x+2y−z+4=0

**Q.**

Draw the graph of the following linear equations in two variables: $x+y=4$

**Q.**An equation of the plane passing through the point (1, -1, 2)and parallel to the plane 3x + 4y - 5z = 0 is

- 3x+4y-5z=11
- 3x+4x-5z+11=0
- 6x+8y-10z=1
- 3x+4y-5z=2

**Q.**

The equation of the plane passing through the lines x−41=y−31=z−22 and x−31=y−2−4=z5 is

11x+y−3z=35

11x−y−3z=35

11x−y+3z=35

None of these

**Q.**

A point is moves on xy plane.If the sum of the distance from two mutual perpendicular lines is 5 then area under it is

**Q.**The least positive value of t, so that the lines x=t+α, y+16=0 and y=αx are concurrent, is:

- 2
- 4
- 16
- 8

**Q.**If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.

**Q.**Reflection of the line x−1−1=y−23=z−41 in the plane x +y +z =7 is :

- x−13=y−21=z−41
- x−1−3=y−2−1=z−41
- x−1−3=y−21=z−4−1
- x+13=y−21=z+41

**Q.**The equation of the plane containing the two lines of intersection of the two pairs of planes x + 2y – z – 3 = 0 and 3x – y + 2z – 1 = 0, 2x – 2y + 3z = 0 and x – y + z + 1 =0 is :

- None of these
- 7x – 7y + 8z + 3 = 0
- 7x – 8y + 9z + 3 = 0
- 5x – 5y + 6z + 2 = 0

**Q.**

Find the equations of the planes that passes through three points.

(a) (1, 1, −1), (6, 4, −5), (−4, −2, 3)

(b) (1, 1, 0), (1, 2, 1), (−2, 2, −1)

**Q.**Find the equation of the plane that contains the point (1, –1, 2) and is perpendicular to each of the planes 2x+3y–2z=5 and x+2y–3z=8.

**Q.**

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along *x*-axis

**Q.**Reflection of the line x−1−1=y−23=z−41 in the plane x +y +z =7 is :

- x−13=y−21=z−41
- x−1−3=y−2−1=z−41
- x−1−3=y−21=z−4−1
- x+13=y−21=z+41

**Q.**30. P is a point(a, b, c) . Let A , B , C be images of P in y_z , z_x and x_y planes respectively , then the equation of the plane ABC is

**Q.**If lx+my+nz = d is the general form of the equation of a plane and l, m, n are direction cosines of that plane, then what does d represent?

- The normal distance of the plane from the origin
- Direction cosine of the z-axis
- Direction cosine of the y-axis
- Direction cosine of the x-axis

**Q.**Find the Cartesian equation of the following planes: (a) (b) (c)

**Q.**

If l, m, n are the direction cosines of the normal to the plane and p be the perpendicular distance of the plane from the origin, then the equation of the plane is:

**Q.**

Find the area of the region bounded by the ellipse

**Q.**The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line (12)x=(13)y=(−16)z is :

- 1
- 2
- 12
- 4

**Q.**Number of solutions for the system of equations x+2y+z=0, 3x+5y+2z=2 and 2x+4y+2z=1

- 1
- infinity
- 2
- 0

**Q.**

What is the cartesian equation of a plane?

**Q.**

If the general equation of plane is given by ax + by + cz = d then a, b, c are the direction ratios of the normal to the plane.

True

False

**Q.**

What is stationary point in maxima and minima?

**Q.**Find the area of the region bounded by y = $\sqrt{x}$ and y = x.