If `A=(0,1)B=(1,0),C=(1,2),D=(2,1)` , prove that ` vec A B= vec C Ddot`

If =(0,1)B=(1,0),C=(1,2),D=(2,1) ,prove that vec AB=vec CD

If A=(1,0,1), B=(0,-1,0), C=(-1,0,1), D=(0,1,-1) then angle between vec(AB) and vec(CD) is (A) pi/6 (B) pi/4 (C) pi/3 (D) pi/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)=(2,1,-1), vec(b)=(1,-1,0), vec(c)=(5, -1,1) , then what is the unit vector parallel to vec(a)+vec(b)-vec(c) in the opposite direction ?

If vec a=(-1,1,2);vec b=(2,1,-1);vec c=(-2,1,3) then the angle between 2vec a-vec c and vec a+vec b is

If vec(a)= (2, 1, -1), vec(b) = (1, -1, 0), c= (5, -1, 1) , then what is the unit vector parallel to vec(a) +vec(b)- vec(c ) in the oppoiste direction?

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a) , prove that vec(a), vec(b), vec(c ) are mutually at right angles and |vec(b)|=1, |vec(c )|=|vec(a)| .

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

Let vec a=hat i+hat j+hat k,vec b=hat i and hat c=c_(1)hat i+c_(2)hat j+c_(3)hat k. Then,(1) If c_(1)=1 and c_(2)=2, find c_(3) which makes vec a,vec b and vec c coplanar.(2) If c_(2)=-1 and c_(3)=1, show that no value of c_(1) can make vec a,vec b and vec c coplanar.