" If "vec V_(1)+vec V_(2)" is perpendicular to "vec V_(1)-vec V_(2)" .then "

A moving particle of mass m collides elastically with a stationary particle of mass 2m . After collision the two particles move with velocity vec(v)_(1) and vec(v)_(2) respectively. Prove that vec(v)_(2) is perpendicular to (2 vec(v)_(1) + vec(v)_(2))

If a charged particle goes unaccelerated in a region containing electric and magnetic fields, (i) vec(E) must be perpendicular to vec(B) (ii) vec(v) must be perpendicular to vec(E) (iii) vec(v) must be perpendicular to vec(B) (iv) E must be equal to v B

If vec V_(1)=hat i+hat j+hat k;vec V_(2)=ahat i+bhat j+chat k where a,b,c in{-2,-1,0,1,2} then the number of non-zero vectors vec V_(2) which perpendicular to (vec V_(1))/(18) is

Let vec a,vec b, and vec c be non-zero vectors and vec V_(1)=vec a xx(vec b xxvec c) and vec V_(2)(vec a xxvec b)xxvec c . Vectors vec V_(1)andvec V_(2) are equal.Then vec a an vec b are orthogonal b.vec a and vec c are collinear c.vec b and vec c are orthogonal d.vec b=lambda(vec a xxvec c) when lambda is a scalar

Let vec(u),vec(v) and vec(w) be such that |vec(u)|=1,|vec(v)|=2,|vec(w)|=3 . If the projection vec(v) along vec(u) is equal to that of vec(w) along vec(u) and vec(v),vec(w) are perpendicular to each orher, then |vec(u)-vec(v)+vec(w)| equals ............... .

If |vec(V)_(1)+vec(V)_(2)|=|vec(V)_(1)-vec(V)_(2)|and V_(2) is finite, then

If |vec(V)_(1)+vec(V)_(2)|=|vec(V)_(1)-vec(V)_(2)|and V_(2) is finite, then

Find 3 -dimensional vectors vec v_ (1), vec v_ (2), vec v_ (3) satisfying vec v_ (1) * vec v_ (1) = 4, vec v_ (1) * vec v_ (2) = - 2, vec v_ (1) * vec v_ (3) = 6, vec v_ (2) * vec v_ (2) = 2, vec v_ (2) * vec v_ (3) = - 5, vec v_ (3) * vec v_ (3)