Home
Class 12
MATHS
If O A B C is a tetrahedron where O is t...

If `O A B C` is a tetrahedron where `O` is the orogin anf `A ,B ,a n dC` are the other three vertices with position vectors, ` vec a , vec b ,a n d vec c` respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector `(a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c])` .

Promotional Banner

Similar Questions

Explore conceptually related problems

If O A B C is a tetrahedron where O is the origin and A ,B ,a n dC are the other three vertices with position vectors, vec a , vec b ,a n d vec c respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector (a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c]) .

If vec a , vec ba n d vec c are the position vectors of the vertices A ,Ba n dC respectively, of A B C , prove that the perpendicular distance of the vertex A from the base B C of the triangle A B C is (| vec axx vec b+ vec bxx vec c+ vec cxx vec a|)/(| vec c- vec b|)dot

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

For any three vectors adotb\ a n d\ c write the value of vec axx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)dot

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

For any three vectors veca , vec b , vec c show that vecaxx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)= vec0

For any three vectors a,b\ a n d\ c write the value of vec axx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)dot

Prove that the normal to the plane containing three points whose position vectors are vec a , vec b , vec c lies in the direction vec bxx vec c+vec cxx vec a+ vec axx vec bdot

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec a.vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec b.vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec c. vec d)/([ vec a vec b vec c])( vec axx vec b)