Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>ADDITIONAL EXERCISES>Q 8

HARD

12th Odisha Board

IMPORTANT

Earn 100

Prove that three lines drawn from origin with direction cosines proportional to $(1, - 1, 1), (2 - 3, 0), (1, 0, 3)$ lie on one plane.

Important Questions on Three Dimensional Geometry

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>ADDITIONAL EXERCISES>Q 9

Determine

k

so that the lines joining the points

P_{1} (k, 1, - 1)

and

P_{2} (2 k, 0, 2)

shall be perpendicular to the line from

P_{2}

to

P_{3} (2 + 2 k, k, 1)

.

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>ADDITIONAL EXERCISES>Q 10

The angle between the lines whose direction ratios are proportional to

a, b, c

and

b - c, c - a, a - b

is of the form of

\frac{π}{a}

, then

a =

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>ADDITIONAL EXERCISES>Q 11

O

is the origin and

A

is the point

(a, b, c)

. Find the equation of the plane through

A

at right angles to

OA

.

HARD

12th Odisha Board

IMPORTANT

Elements of Mathematics Class 12>Chapter 13 - Three Dimensional Geometry>ADDITIONAL EXERCISES>Q 12

Find the equation of the plane through $(6, 3, 1)$ and $(8, - 5, 3)$ parallel to $x -$ axis.