Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 4

HARD

12th Odisha Board

IMPORTANT

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Write the symmetric form of equation of the line: $ax + by + d = 0, 5 z = 0$

Important Questions on Three Dimensional Geometry

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 4

Write the symmetric form of equation of the following lines :

$x - 2 y = 3, 2 x + y - 5 z = 0;$

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 4

Write the symmetric form of equation of line:

$4 x + 4 y - 5 z - 12 = 0 = 8 x + 12 y - 13 z - 32;$

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 4

Write the symmetric form of equation of line:

$3 x - 2 y + z = 1, 5 x + 4 y - 6 z = 2;$

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 5

Obtain the equation of the line p through the point

(1, 2, 3)

, and parallel to the line

x - 2 y + 2 z - 5 = 0 = 3 x + y + z - 6

.

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 5

Find the equation of the line through the point

(3, - 1, 2)

, and parallel to the plane

x + y + 2 z - 4 = 0

and

2 x - 3 y + z + 3 = 0

.

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 6

Obtain the equation of the line through the point

(0, 2, - 3)

, and perpendicular to each of the lines

x + 4 y - 3 z = 0 = 2 x - 5 y + 7 and y + 3 z - 2 = 0 = x + 2 z + 5

.

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 7

Show that the line passing through the points

(a_{1}, b_{1}, c_{1})

, and

(a_{2}, b_{2}, c_{2})

, passes through the origin, if

a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = p_{1} p_{2}

, where

p_{1}

and

p_{2}

, are distances of the points from origin.

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>EXERCISES -13(C)>Q 7

Prove that the lines

x = az + b, y = cz + d and x = a_{1} z + b_{1}, y = c_{1} z + d_{1}

, are perpendicular if

{aa}_{1} + {cc}_{1} + 1 = 0

.