RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 14

HARD

12th West Bengal Board

IMPORTANT

Earn 100

A plane meets the co-ordinate axes at $A, B, C$ and the centroid of the triangle $A B C$ is at $C (p, q, r)$ . Show that the equation of the plane is $\frac{x}{p} + \frac{y}{q} + \frac{z}{r} = 3$ .

Important Questions on The Plane

MEDIUM

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 15

A variable plane which remains at a constant distance

3 p

from the origin cut the coordinate axes at

A, B, C

. Show that the locus of the centroid of the triangle

A B C

is

\frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}} = \frac{1}{p^{2}}

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 16

Show that

(\frac{1}{8}, \frac{1}{8}, \frac{1}{8})

is the centroid of the tetrahedron formed by the planes

x = 0, y = 0, z = 0

and

2 x + 2 y + 2 z = 1

.

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 17

Find the equation of the plane passing through the points

(3, 4, - 1)

and parallel to the plane

2 x - 3 y + 5 z + 7 = 0

and find the distance between the planes.

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 18

Find the distance between the planes

2 x - y + 2 z - 7 = 0

and

2 x - y + 2 z + 8 = 0

.

MEDIUM

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 19

Find the distance of the point

(3, 3, 3)

from the plane

\vec{r} \cdot (5 \hat{i} + 2 \hat{j} - 7 \hat{k}) + 9 = 0

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 20

Find the locus of a point, the sum of the squares of whose distances from the planes

x + y + z = 0, x - y = 0

and

x + y - 2 z = 0

is

4 unit

.

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 1

The line

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

is parallel to the plane

\vec{r} \cdot (3 i - 2 j + m k) = 7

, then the value of

m

is _____

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 25 - The Plane>EXERCISE>Q 1

The angle between the line

\vec{r} = 2 i + 3 j + 9 k + λ (2 i + 3 j + 4 k)

and the plane

r \cdot (i + j + k) = 5

is of the form of

\sin^{- 1} (\frac{3 \sqrt{3}}{\sqrt{a}})

, then

a =

_____