Home
Class 12
MATHS
Points A( vec a),B( vec b),C( vec c)a n ...

Points `A( vec a),B( vec b),C( vec c)a n dD( vec d)` are relates as `x vec a+y vec b+z vec c+w vec d=0` and `x+y+z+w=0,w h e r ex ,y ,z ,a n dw` are scalars (sum of any two of `x ,y ,zn a dw` is not zero). Prove that if `A ,B ,Ca n dD` are concylic, then `|x y|| vec a- vec b|^2=|w z|| vec c- vec d|^2dot`

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

For any three vectors vec a, vec b , vec c , show that vec a xx (vec b + vec c) + vec b xx (vec c + vec a) + vec c xx (vec a + vec b) = 0

Prove that if the vectors vec a, vec b, vec c satisfy vec a+ vec b + vec c = vec 0 , then vec bxx vec c = vec c xx vec a = vec a xx vec b

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d)dot (vec b- vec c)!=0,

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec ca n d vec a is not a zero vector. Show that vec b= vec cdot

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

Given that vec a , vec b , vec p , vec q are four vectors such that vec a+ vec b=mu vec p , vec b*vec q=0a n d|vec b|^2=1,w h e r emu is a scalar. Then |( vec adot vec q) vec p-( vec pdot vec q) vec a| is equal to (a) 2| vec p . vec q| (b) (1//2)| vec p . vec q| (c) | vec pxx vec q| (d) | vec p . vec q|

If vec a , vec b ,a n d vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c|dot

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=0