" easy "vec " Of "" ।ा ":(1)quad 2^((2)/(3))*2^((1)/(5))

If | vec a| = | vec b | = 1 and | vec a + vecb | = sqrt3 , then the value of (3 veca -4 vec b ).(2veca +5vec b ) is : a) -21 b) -(21)/(2) c) 21 d) (21)/(2)

If vec A=(1,1,1),vec C=(0,1,-1) are given vectors,then prove that a vector vec B satisfying the equations vec A xxvec B=vec C and vec A*vec B=3 is ((5)/(3),(2)/(3),(2)/(3))

If vec A_(1) and vec A_(2) are two non-collinear unit vectors and if |vec A_(1)+vec A_(2)|=sqrt(3) then the value of (vec A_(1)-vec A_(2))*(2vec A_(1)+vec A_(2)) is

If vec(a_(1)),vec(a_(2)),vec(a_(3)) and vec(b_(1)), vec(b_(2)),vec(b_(3)) be two sets of non - coplanar vectors, such that vec(a_(p)).vec(b_(q))={{:(0,"if",pneq),(4,"if",p=q):}" for "p=1,2,3 and q=1,2,3 , then the value of [vec(a_(1))2vec(a_(2))3vec(a_(3))][(vec(b_(1))+vec(b_(2)),vec(b_(2))+vec(b_(3)),vec(b_(3)),vec(b_(3))+vec(b_(1)))] is equal to

If vec(a_(1)) and vec(a_(2)) are two non-collinear unit vectors and if |vec(a_(1)) + vec(a_(2))|=sqrt(3) , then the value of (vec(a_(1))-vec(a_(2))). (2 vec(a_(1))+vec(a_(2))) is :

If vec(a_(1)) and vec(a_(2)) are two non-collinear unit vectors and if |vec(a_(1)) + vec(a_(2))|=sqrt(3) , then the value of (vec(a_(1))-vec(a_(2))). (2 vec(a_(1))+vec(a_(2))) is :

For anyy two vectors vec(a) and vec(b) , show that (1+|vec(a)|^(2))(1+|vec(b)|^(2))= |(1-vec(a).vec(b))|^(2)+|vec(a)+vec(b)+(vec(a)xx vec(b))|^(2)

If vec a=hat i+hat j+hat k=hat i-2hat j+hat k and the vector vec c such that vec a*vec c=2 and vec axvec c=vec b then vec c is (1)/(3)(hat i-2vec j+vec k) (2) (1)/(3)(-hat i+2hat j+5hat k)(1)/(3)(hat i+2hat j-5hat k)(4)(1)/(3)(-hat i+2hat j-5hat k)

Find a vector of magnitude sqrt(51) and makes equal angle with the vectors vec(a)=(1)/(3)(hati-2hatj+2hatk),vec(b)=(1)/(5)(-4hati-3hatk) and vec( c )=hatj .