Prove that in a tetrahedron if two pa...

Prove that in a tetrahedron if two pairs of opposite edges are perpendicular , then the third pair is also perpendicular.

Topper's Solved these Questions

TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS
CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos
VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS
CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

Prove that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

prove that the diagonals of a rhombus are perpendicular to each other.

Prove that the tangent and the radius through the point of contact of a circle are perpendicular to each other.

A straight line moves so that the product of the length of the perpendiculars on it from two fixed points is constant. Prove that the locus of the feet of the perpendiculars from each of these points upon the straight line is a unique circle.

Prove that if two opposite angles and two opposite sides of any quadrilateral be parallel , then it is a parallelogram.

The electric and magnetic field of electromagnetic waves are- in opposite phase and perpendicular to each other in oppopsite phase and parallel to each other in the same phase and perpendicular in the same phase and parallel to each other.

What is the scalar product of two vectors perpendicular to each other ?

Prove that the tangent to the circle at any point on it is perpendicular to the radius passes through the point of contact.

The locus of the point of intersection of a pair of perpendicular tangents to an ellipse is a/an-

Find the equation to the perpendicular bisector of the line -segment joining the two points (2,3) and (4,-1). What is the length of the perpendicular drawn from the origin to that perpendicular bisector ?

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions

If vec a and vec b are two vectors, then prove that ( vec axx vec b...
Text Solution
|
In isosceles triangles A B C ,| vec A B|=| vec B C|=8, a point E divid...
Text Solution
|
Prove that in a tetrahedron if two pairs of opposite edges are perp...
Text Solution
|
Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec ...
Text Solution
|
If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a...
Text Solution
|
If vec A=4 hat i+6 hat j and vec B=3 hat j+4 hat k , then find the co...
Text Solution
|
A particle acted by constant forces 4 hat i+ hat j-3 hat k and 3 hat...
Text Solution
|
If veca , vecb , vecc are three mutually perpendicular unit ve...
Text Solution
|
Let vec a=x hat i+12 hat j- hat k , vec b=2 hat i+2x hat j+ hat ka n ...
Text Solution
|
If vec a , vec b ,a n d vec c are three non-coplanar vectors, then ...
Text Solution
|
If vec a , vec b , vec ca n d vec d are the position vectors of the...
Text Solution
|
The position vectors of the vertices of a quadrilateral with A as o...
Text Solution
|
If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , t...
Text Solution
|
Show by a numerical example and geometrically also that vec axx ve...
Text Solution
|
In triangle A B C ,points D , Ea n dF are taken on the sides B C ,C Aa...
Text Solution
|
Let A ,B ,C be points with position vectors 2 hat i- hat j+ hat k , ...
Text Solution
|
Let vec a and vec b be unit vectors such that | vec a+ vec b|=sqrt(3)...
Text Solution
|
If u and v are two non-collinear unit vectors such that |vecu...
Text Solution
|
A rigid body is spinning about a fixed point (3,-2,-1) with an angu...
Text Solution
|
vec rxx vec a= vec bxx vec a ; vec rxx vec b= vec axx vec b ; vec a!= ...
Text Solution
|