Home
Class 12
MATHS
In a regular tetrahedron, let theta be a...

In a regular tetrahedron, let `theta` be angle betweenn any edge and a face not containing the edge. The value of `cos^(2)theta` is

A

`1//6`

B

`1//9`

C

`1//3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let OABC be the tetrahedron. Let G be the centorid of the face OAB, then `GA=1/sqrt(3)AC`.

Then `costheta=(GA)/(CA)=1/sqrt(3)`
`therefore cos^(2)theta=1/3`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives(Matrix Match Type)|1 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE ENGLISH|Exercise Archives|1 Videos

Similar Questions

Explore conceptually related problems

In a regular tetrahedron, let theta be angle between any edge and a face not containing the edge. Then the value of cos^(2)theta is

In a regular tetrahedron, prove that angle theta between any edge and the face not containing that edge is given by cos theta = 1/sqrt3 .

Let k be the length of any edge of a regular tetrahedron (a tetrahedron whose edges are equal in length is called a regular tetrahedron). Show that the angel between any edge and a face not containing the edge is cos^(-1)(1//sqrt(3)) .

Let k be the length of any edge of a regular tetrahedron (a tetrahedron whose edges are equal in length is called a regular tetrahedron). Show that the angel between any edge and a face not containing the edge is cos^(-1)(1//sqrt(3)) .

Comprehesion-I Let k be the length of any edge of a regular tetrahedron (all edges are equal in length). The angle between a line and a plane is equal to the complement of the angle between the line and the normal to the plane whereas the angle between two plane is equal to the angle between the normals. Let O be the origin and A,B and C vertices with position vectors veca,vecb and vecc respectively of the regular tetrahedron. The angle between any edge and a face not containing the edge is

find the height of the regular pyramid with each edge measuring l cm. Also, (i) if alpha is angle between any edge and face not containing that edge, then prove that cosalpha=1/sqrt3 (ii) if beta is the between the two faces, then prove that cosbeta=1/3

In a regular tetrahedron, if the distance between the mid points of opposite edges is unity, its volume is

Comprehesion-I Let k be the length of any edge of a regular tetrahedron (all edges are equal in length). The angle between a line and a plane is equal to the complement of the angle between the line and the normal to the plane whereas the angle between two plane is equal to the angle between the normals. Let O be the origin and A,B and C vertices with position vectors veca,vecb and vecc respectively of the regular tetrahedron. The angle between any two faces is

Comprehesion-I Let k be the length of any edge of a regular tetrahedron (all edges are equal in length). The angle between a line and a plane is equal to the complement of the angle between the line and the normal to the plane whereas the angle between two plane is equal to the angle between the normals. Let O be the origin and A,B and C vertices with position vectors veca,vecb and vecc respectively of the regular tetrahedron. The value of [vecavecbvecc]^(2) is

ABCD is a regular tetrahedron P & Q are the mid -points of the edges AC and AB respectively, G is the cenroid of the face BCD and theta is the angle between the vectors vec(PG) and vec(DQ) , then