Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

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For a map with a scale of 1:25,000, what is the ground distance represented by 4 cm on the map?

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Important Questions on Introduction to Three Dimensional Geometry

HARD

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The

H^{+}

ion concentration of a solution is

2 \times 10^{- 8} mol L^{- 1}

. The pH value of the solution is

\log_{10} 2 = 0.3010

.

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

Locus of the centre of rolling circle in a plane will be

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The length of the perpendicular drawn from the point

(4, - 7, 3)

on the

y -

axis is

HARD

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

Vertices of a triangle are

(3, 2, - 5), (- 3, 8, - 5)

and

(3, 2, - 1)

. Show that its circumcentre is

(0, 5, - 3)

MEDIUM

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The points

A (- 2, 6, - 2), B (0, 4, - 1), C (- 2, 3, 1)

and

D (- 4, 5, 0)

are the vertices of

MEDIUM

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

Find the distance of the point

(- 1, - 5, - 10)

from the point of intersection of the line

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

and the plane

\vec{r} \cdot (\hat{i} - \hat{j} + \hat{k}) = 5 .

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

Find the length and the foot of the perpendicular from the point

(1, 1, 2)

to the plane

\vec{r} \cdot (\hat{i} - 2 \hat{j} + 4 \hat{k}) + 5 = 0 .

MEDIUM

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The locus of the point

P (x, y, z)

which moves such that it is equidistant from

A (- 3, 3, 1)

and

B (0, 2, 1)

is

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

If the coordinate of the verities of a triangle

A B C

be

A (- 1,3, 2), B (2,3, 5) & C (3,5, - 2),

then

∠ A

is equal to

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The point equidistant from the point (

a, 0, 0

),

(0, b, 0), (0, 0, c)

and

(0, 0, 0)

is

MEDIUM

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

In the given figure, AM is the median of △ ABC.

Question Image

Question Image

What is the length of AM?

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The distance of the point

(2, 3, 4)

from origin

(0, 0, 0)

is

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Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The points

A (5, - 1,1), B (7, - 4,7), C (1, - 6,10)

and

D (- 1, - 3, 4)

are vertices of a

MEDIUM

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

A

and

B

are the points

(2, 3, 4)

and

(- 2, 5, - 4)

. If

P (x, y, z)

is moving such that

A P = P B

, then the locus of the point

P

is.

MEDIUM

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The perpendicular distance of the point

(6, 5, 8)

from

y

-axis is

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The distance between the points

(1, 4, 5)

and

(2, 2, 3)

is

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The distance[Units] of the points

(- 2, 4, 1)

and

(1, 2, 5)

is of the form

\sqrt{a}

, then

a =

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

A point on the

x

-axis is at a distance of

5 \sqrt{2}

units from

(3, 4, - 3)

is

EASY

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

Consider points

A, B, C

and

D

with position vectors

7 \hat{\dot{i}} - 4 \hat{\dot{j}} + 7 \hat{k}, \hat{\dot{i}} - 6 \hat{\dot{j}} + 10 \hat{k}

,

- \hat{\dot{i}} + 3 \hat{\dot{j}} + 4 \hat{k}

and

5 \hat{\dot{i}} - \hat{\dot{j}} + 5 \hat{k}

respectively. Then,

A B C D

is a

MEDIUM

Mathematics>Coordinate Geometry>Introduction to Three Dimensional Geometry>Distance Formula in 3D

The points (5, -4, 2), (4, -3, 1), (7, -6, 4) and (8, -7, 5) are the vertices of