MEDIUM

Earn 100

Find the equation of the plane passing through the point $(1, 1, 2)$ having $2, 3, 2$ as direction ratios of normal to the plane.

50% studentsanswered this correctly

Important Questions on Three Dimensional Geometry

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

Equation of the plane which passes through the point of intersection of lines

\frac{x - 1}{3} = \frac{y - 2}{1} = \frac{z - 3}{2}

and

\frac{x - 3}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}

and has the largest distance from the origin is:

EASY

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

A plane is at a distance of

5

units from the origin and perpendicular to the vector

2 \hat{i} + \hat{j} + 2 \hat{k}

.

The equation of the plane is

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The coordinates of the foot of the perpendicular from the point

(1, - 2, 1)

on the plane containing the lines

\frac{x + 1}{6} = \frac{y - 1}{7} = \frac{z - 3}{8}

and

\frac{x - 1}{3} = \frac{y - 2}{5} = \frac{z - 3}{7},

is:

MEDIUM

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

A plane passing though the points

(0, - 1, 0)

and

(0, 0, 1)

and making an angle

\frac{π}{4}

with the plane

y - z + 5 = 0,

also passes through the point

EASY

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The equation of the plane which bisects the line joining

(3, 0, 5)

and

(1, 2, - 1)

at right angles is

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The equation of the plane passing through the point

(1,1, 1)

and perpendicular to the planes

2 x + y - 2 z = 5

and

3 x - 6 y - 2 z = 7

EASY

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The equation of the plane passing through the points

(1, 2, 3), (- 1, 4, 2)

and

(3, 1, 1)

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The plane passing through the points

(1, 2, 1), (2, 1, 2)

and parallel to the line,

2 x = 3 y

z = 1

also passes through the point

MEDIUM

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The sum of the intercepts on the coordinate axes of the plane passing through the point

(- 2, - 2, 2)

and containing the line joining the points

(1, - 1, 2)

and

(1, 1, 1)

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The distance of the point

(1, 3, - 7)

from the plane passing through the point

(1, - 1, - 1)

, having normal perpendicular to both the lines

\frac{x - 1}{1} = \frac{y + 2}{- 2} = \frac{z - 4}{3}

and

\frac{x - 2}{2} = \frac{y + 1}{- 1} = \frac{z + 7}{- 1}

, is:

MEDIUM

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The length of the perpendicular drawn from the point

(2, 1, 4)

to the plane containing the lines

\vec{r} = (\hat{i} + \hat{j}) + λ (\hat{i} + 2 \hat{j} - \hat{k})

and

\vec{r} = (\hat{i} + \hat{j}) + μ (- \hat{i} + \hat{j} - 2 \hat{k})

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The equation of the plane containing the straight line

\frac{x}{2} = \frac{y}{3} = \frac{z}{4}

and perpendicular to the plane containing the straight lines

\frac{x}{3} = \frac{y}{4} = \frac{z}{2}

and

\frac{x}{4} = \frac{y}{2} = \frac{z}{3}

is:

EASY

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

If the foot of the perpendicular drawn from the point

(0, 0, 0)

to the plane is

(4, - 2, - 5)

then the equation of the plane is …..

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

L_{1}

is the line of intersection of the planes

2 x - 2 y + 3 z - 2 = 0, x - y + z + 1 = 0

and

L_{2}

is the line of intersection of the planes

x + 2 y - z - 3 = 0, 3 x - y + 2 z - 1 = 0,

then the distance of the origin from the plane, containing the lines

L_{1}

and

L_{2}

MEDIUM

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The plane which bisects the line joining the points

(4, - 2, 3)

and

(2, 4, - 1)

at right angles also passes through the point :

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The combined equation for a pair of planes is

S \equiv 2 x^{2} - 6 y^{2} - 12 z^{2} + 18 y z + 2 z x + x y = 0 .

If one of the planes is parallel to

x + 2 y - 2 z = 5,

then the acute angle between the planes

S = 0

EASY

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

If a variable plane in

3

-dimensional space moves in such a way that the sum of the reciprocals of its intercepts on the

x

and

y

-axes exceeds the reciprocal of its intercept on the

z

-axis by

2

, then all such planes will pass through the point

EASY

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The equation of the plane through

(- 1, 1, 2),

whose normal makes equal acute angle with co-ordinate axes is

HARD

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

Let

P_{1} : 2 x + y - z = 3 a n d P_{2} : x + 2 y + z = 2

be two planes. Then, which of the following statement(s) is (are) TRUE?

MEDIUM

Mathematics>Coordinate Geometry>Three Dimensional Geometry>Plane

The plane passing through the point

(4, - 1, 2)

and parallel to the lines

\frac{x + 2}{3} = \frac{y - 2}{- 1} = \frac{z + 1}{2}

and

\frac{x - 2}{1} = \frac{y - 3}{2} = \frac{z - 4}{3}

also passes through the point

Find the equation of the plane passing through the point 1,1,2 having 2,3,2 as direction ratios of normal to the plane.

Important Questions on Three Dimensional Geometry

Learn and Prepare for any exam you want !

Find the equation of the plane passing through the point $(1, 1, 2)$ having $2, 3, 2$ as direction ratios of normal to the plane.