ABCDE is a pentagon .prove that the resultant of force ` vec A B ,` ` vec A E` ,` vec B C` ,` vec D C` ,` vec E D` and ` vec A C` ,is 3` vec A C` .

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

In a regualr hexagon ABCDEF, A vecB = vec a, B vec C = vecb and C vec D = vec c. " Then " A vec E =

[vec a, vec b + vec c, vec d] = [vec a, vec b, vec d] + [vec a, vec c, vec d]

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to

Give vec A + vec B+ vec C + vec D =0 , which of the following statements are correct ? (a) vec A, vec B ,vec C abd vec C must each be a null vector. (b) The magnitude of ( vec A + vec C) equals the magnitude of ( vec B + vec D0 . ltBrgt (c ) The magnitude of vec A can never be greater than the sum of the magnitude of vec B , vec C and vec D . ( d) vec B + vec C must lie in the plance of vec A + vec D. if vec A and vec D are not colliner and in the line of vec A and vec D , if they are collinear.

[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

Prove that,for any three vectors vec a,vec b,vec c[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

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)

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =