Is ` | vec A + vec B|` greater than or less than ` |vec A| + |vec B| `? Explain.

Is |vec A - vec B| greater than or less than |vec A| + |vec B| ? Explain.

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.

If vec a, vec b , and vec c are vectors such that |vec b| = |vec c| , then {[(vec a + vec b) xx (vec a + vec c)] xx (vec b xx vec c)} . (vec b + vec c) =

if | vec a | = | vec b | = | vec a + vec b | = 1 then | vec a-vec b |

If vec a and vec b are two vectors, then prove that ( vec axx vec b)^2=|[vec a.vec a,vec a.vec b],[vec b.vec a,vec b.vec b]| .

If vec a and vec b are two vectors, then prove that ( vec axx vec b)^2=|[vec a.vec a,vec a.vec b],[vec b.vec a,vec b.vec b]| .

If vec a ,\ vec b ,\ vec c are three vectors such that vec a. vec b= vec a.\ vec c and vec a\ xx\ vec b= vec a\ xx\ vec c ,\ vec a\ !=0 , then show that vec b= vec c .

Given vec A+ vec B+ vec + vec D=0 , can the magnitude of vec A + vec B + vec C be equal to the magnitude of vec D Explain.

if | vec a | = | vec b | then find [(vec a + vec b) * (vec a-vec b)]

If vec a and vec b are two vectors such that vec a + vec b is perpendicular to vec a - vec b ,then prove that |vec a| = |vec b| .