Let `vecu and vecv` be unit vectors. If `vecw` is a vector such that `vecw+vecwxxvecu=vecv`, then prove that `|(vecuxxvecv).vecw|le1/2` and that the equality holds if and only if `vecu` is perpendicular to `vecv`.

Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(veca.vecb)vecb and vecv=vecaxxvecb , then |vecv| is

If vecu and vecv are unit vectors and theta is the acute angle between them, then 2 vecu xx 3vecv is a unit vector for

Let veca and vecb be two unit vectors. If the vectors : vecc=veca+2vecb and vecd=5veca-4vecb are perpendicular to each other, then the angle between veca and vecb is :

Let A,B and C be unit vectors . Suppuse that A.B=A.c=O and that the angle between Band C is pi//6 then prove that A=+-2(BxxC)

Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d| vec w|=3. If the projection of vec v along vec u is equal to that of vec w along vec u and vectors vec va n d vec w are perpendicular to each other, then | vec u- vec v+ vec w| equals a 2 b. sqrt(7) c. sqrt(14) d. 14

If veca and vecb are unit vectors inclined at an angle theta then prove that cos(theta/2) = 1/2|veca +vecb|

If unit vectors veca and vecb are inclined at an angle 2 theta such that |veca - vecb| lt 1 and 0 le theta le pi , then theta lies in the interval

Let vec A , vec B , vec C be unit vectors. Suppose that vec A*vec B=vec A*vec C=0 and the angle between vec B and vec C is pi/6 . Prove that vec A=pm 2(vec Bxxvec C) .

Let vec u=hat i+hat j,vec v=hat i-hat j and vec w=hat i+2 hat j+3hat k .If hat n is a unit vector such that vec u*hat n=0 and vec v*hat n=0 then |vec w*hat n| is equal to

Let a,b,c denote the lengths of the sides of a triangle such that ( a-b) vecu + ( b-c) vecv + ( c-a) (vecu xx vecv) = vec0 For any two non-collinear vectors vecu and vecv ,then the triangle is