The locus of a point, which moves in such a way that its distance from the line x 1 = y 1 = z - 1 is twice the distance from the plane x + y + z = 0 is

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

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

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

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

HARD

JEE Advanced

IMPORTANT

Earn 100

A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have length $13, 19, 20, 25$ and $31$ not necessarily in that order. The area of the pentagon is

50% studentsanswered this correctly

Important Questions on Three Dimensional Coordinate System

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 3 - Three Dimensional Coordinate System>Three Dimensional Coordinate System Exercise 1>Q 80

In a three-dimensional coordinate system

P, Q, R

are images of a point

A (a, b, c)

in the

X Y, Y Z & Z X

planes respectively. If

G

is the centroid of triangle

P Q R

, then area of triangle

A O G

is (

O

is the origin)

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 3 - Three Dimensional Coordinate System>Three Dimensional Coordinate System Exercise 1>Q 81

A plane

2 x + 3 y + 5 z = 1

has a point

P

, which is at minimum distance from line joining

A (1, 0, - 3), B (1, - 5, 7)

, then distance

A P

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 3 - Three Dimensional Coordinate System>Three Dimensional Coordinate System Exercise 1>Q 82

The locus of a point, which moves in such a way that its distance from the line

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

is twice the distance from the plane

x + y + z = 0

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 3 - Three Dimensional Coordinate System>Three Dimensional Coordinate System Exercise 1>Q 83

A cube

C = \{(x, y, z) / 0 \leq x, y, z \leq 1\}

is cut by a sharp knife along the plane

x = y, y = z, z = x

. If no piece is moved until all three cuts are made, the number of pieces is

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 3 - Three Dimensional Coordinate System>Three Dimensional Coordinate System Exercise 1>Q 84

A ray of light is sent through the point

P (1, 2, 3)

and is reflected on the

X Y

-plane. If the reflected ray passes through the point

Q (3, 2, 5)

, then equation of the reflected ray is

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 3 - Three Dimensional Coordinate System>Three Dimensional Coordinate System Exercise 1>Q 85

A plane cutting the axes in

P, Q, R

passes through

(α - β, β - γ, γ - α)

. If

O

is the origin, then locus of centre of sphere

O P Q R

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 3 - Three Dimensional Coordinate System>Three Dimensional Coordinate System Exercise 1>Q 86

The shortest distance between any two opposite edges of the tetrahedron formed by planes

x + y = 0, y + z = 0, z + x = 0, x + y + z = a, a > 0

is a constant and is equal to

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 3 - Three Dimensional Coordinate System>Three Dimensional Coordinate System Exercise 1>Q 88

Let

(p, q, r)

be a point on the plane

2 x + 2 y + z = 6

, then the least value of

p^{2} + q^{2} + r^{2}

is equal to

A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have length 13, 19, 20, 25 and 31 not necessarily in that order. The area of the pentagon is

Important Questions on Three Dimensional Coordinate System

Learn and Prepare for any exam you want !

A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have length $13, 19, 20, 25$ and $31$ not necessarily in that order. The area of the pentagon is