[" 4.If "vec a=vec b+vec c," then is it true that "|vec a|=|vec b|+|vec c|" ? Justify your answer."]

If veca = vec b+ vec c , then is it true that |veca| = |vec b| + |vec c| ? Justify your answer.

If vec(a)=vec(b)+vec(c ) , then is it true that |vec(a)|=|vec(b)|+|vec(c )| ? Justify your answer.

If either vec a= vec 0 and vec b= vec 0 then vec axx vec b= vec0 . Is Is the converse true? Justify your answer with an example.

If either vec a = vec 0 or vec b = vec0 , then vec a xx vecb = vec 0 . Is the converse true ? Justify your answer with an example.

[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 ) , then |vec(a)|=|vec(b)+vec(c )| .

If either vec a=vec 0 or vec b=vec 0 then vec avec b=vec 0 but, the converse need not be true.Justify your answer with an example.

If vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c= vec0, then write the value of vec a . vec b+ vec b . vec c+ vec c . vec a

If either vec a=0 and vec b=0 then vec a xxvec b=0 Is Is the converse true? Justify your answer with an example.

Let vec a,vec b, and vec c are vectors such that |vec a|=3,|vec b|=4 and |vec c|=5, and (vec a+vec b) is perpendicular to vec c,(vec b+vec c) is perpendicular to vec a and (vec c+vec a) is perpendicular to vec b. Then find the value of |vec a+vec b+vec c|