VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 50

EASY

JEE Advanced

IMPORTANT

Earn 100

Find the distance of the point $(- 6, 0, 0)$ from the plane $2 x - 3 y + 6 z - 2 = 0$ .

50% studentsanswered this correctly

Important Questions on Plane

EASY

JEE Advanced

IMPORTANT

VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 50

Find the distance (in units) of point

(2, 3, - 5)

from the plane

x + 2 y - 2 z = 9

.

MEDIUM

JEE Advanced

IMPORTANT

VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 50

Find the distance of the point

(0, 0, 0)

from the plane

3 x - 4 y + 12 z = 3

.

MEDIUM

JEE Advanced

IMPORTANT

VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 52

If a plane has intercepts

a, b and c

on axes and is at a distance of

p

units from the origin, then prove that

\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} = \frac{1}{p^{2}}

.

HARD

JEE Advanced

IMPORTANT

VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 53

Find the distance between the point

P (6, 5, 9)

and the plane determined by the points

A (3, - 1, 2), B (5, 2, 4)

and

C (- 1, - 1, 6)

.

HARD

JEE Advanced

IMPORTANT

VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 54

Find the distance between the planes

2 x + 3 y + 4 z = 4

and

4 x + 6 y + 8 z = 12

.

HARD

JEE Advanced

IMPORTANT

VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 55

Find the equation of the line of intersection of the planes

x - 2 y + z = 1

and

x + 2 y - 2 z = 5

in symmetric form :

HARD

JEE Advanced

IMPORTANT

VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 56

Find the equation of the line through point

(1, 2, 3)

and parallel to planes

x - y + 2 z = 5, 3 x + y + z = 6

.

HARD

JEE Advanced

IMPORTANT

VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 8 - Plane>EXERCISE>Q 57

Prove that the lines

x = a y + b, z = c y + d

and

x = a^{'} y + b^{'}, z = c^{'} y + d^{'}

are mutually perpendicular if

a a^{'} + c c^{'} = - 1

.