If `|vecA xx vec B|= sqrt3 vecA . vec B` then show that.`|vecA +vec B| = (A^2 + B^2 + AB)^(1/2)`.

If |vecAxxvecB|=sqrt(3)vecA*vecB , then show that |vecA+vecB|=sqrt(A^2+B^2+AB) .

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

Given | vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3). If vec c is a vector such that vec c- vec a-2 vec b=3( vec axx vec b), then find the value of vec c. vec b

If vec A, vec B and vec C are vectors such that |vec B|=|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

If vec a, vec b, vec c are unit vectors satisfying the condition veca+ vec b+ vec c= 0 then show that vec a. vec b+ vec b.vec c+ vec c. vec a= -3//2 .

If vec(a) + vec(b) + vec (c ) = vec(0) , show that vec(a) xx vec(b) = vec(b) xx vec(c ) = vec(c ) xx vec(a)

For any two vectors veca and vec b show that |vec a.vec b|le |vec a|.|vecb|

If vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=sqrt3\ a n d\ vec adot vec b=1, find the angle between vec a\ a n d\ vec b .

Define unit vector vec A and vec B are two vectors and theta is the angle between them. If |vecA xx vecB | = sqrt3(vecA.vecB) , Calculate the value of theta .

If vec a and vec b are unequal unit vectors such that ( vec a- vec b)xx[( vec b+ vec a)xx(2 vec a+ vec b)]= vec a+ vec b , then angle theta between vec aa n d vec b is 0 b. pi//2 c. pi//4 d. pi