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 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 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| .

If vec a and vec b are unit vectors such that |vec a xx vec b| = vec a . vec b , then |vec a + vec b|^(2) =

If vec A, vec B and vec C are vectors such that |vec B|-|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

If vec A, vec B and vec C are vectors such that |vec B|=|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

If vec A, vec B and vec C are vectors such that |vec B|=|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0