A = l 1 m 1 n 1 l 2 m 2 n 2 l 3 m 3 n 3 and B = p 1 q 1 r 1 p 2 q 2 r 2 p 3 q 3 r 3 p i , q i , r i are the cofactors of the elements l i , m i , n i for i = 1 ,2 , 3 . If l 1 , m 1 , n 1 , l 2 , m 2 , n 2 and l 3 , m 3 , n 3 are the direction cosines of three mutually perpendicular lines, then p 1 , q 1 , r 1 , p 2 , q 2 , r 2 and p 3 , q 3 , r 3 are

the direction ratios of three mutually perpendicular lines which are not direction cosines

the direction cosines of three lines which need not be perpendicular

the direction ratios but not the direction cosines of three lines which need not be perpendicular

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IMPORTANT

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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

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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 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

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 89

The four lines drawing from the vertices of any tetrahedron to the centroid of the opposite faces meet in a point whose distance from each vertex is

k

times the distance from each vertex to the opposite face, where

k

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 90

The shortest distance from

(1, 1, 1)

to the line of intersection of the pair of planes

x y + y z + z x + y^{2} = 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 91

The shortest distance between the two lines

L_{1} : x = k_{1}; y = k_{2} & L_{2} : x = k_{3}; y = k_{4}

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 92

A = [\begin{matrix} l_{1} & m_{1} & n_{1} \\ l_{2} & m_{2} & n_{2} \\ l_{3} & m_{3} & n_{3} \end{matrix}]

and

B = [\begin{matrix} p_{1} & q_{1} & r_{1} \\ p_{2} & q_{2} & r_{2} \\ p_{3} & q_{3} & r_{3} \end{matrix}]

p_{i}, q_{i}, r_{i}

are the cofactors of the elements

l_{i}, m_{i}, n_{i}

for

i = 1,2, 3 .

(l_{1}, m_{1}, n_{1}), (l_{2}, m_{2}, n_{2})

and

(l_{3}, m_{3}, n_{3})

are the direction cosines of three mutually perpendicular lines, then

(p_{1}, q_{1}, r_{1}), (p_{2}, q_{2}, r_{2})

and

(p_{3}, q_{3}, r_{3})

are

A cube C=x, y, z/0≤x, y, z≤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

Important Questions on Three Dimensional Coordinate System

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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