Prove that `( -> a+ -> b)dot( -> a+ -> c)| -> a|^2+| -> b|^2` , if and only if ` -> a , -> b` are perpendicular, given ` -> a!= ->0, -> b!= ->0`

Prove that ( veca+ vec b).( vec a+ vecb)= | veca|^2+| vec b|^2 , if and only if vec a ,vec b are perpendicular, given vec a!= vec0, vec b!= vec0

Prove that (vec a + vec b).(vec a + vec b) = | vec a|^(2) + |vec b|^(2) , if and only if vec a, vec b are perpendicualr, given a ne vec 0, b ne vec 0 .

Prove that (vec a+vec b)*(vec a+vec b)=|vec a|^(2)+|vec b|^(2) and only if vec a,vec b are perpendicular,given vec a!=vec 0,vec b!=vec 0

Prove that (veca+vecb).(veca+vecb)=|veca|^2+|b|^2 if and only if veca,vecb are perpendicular, given veca!=vec0"and"vecb!=0 .

Prove that (vec(a)+vec(b)).(vec(a)+vec(b)) = |vec(a)|^(2) + |vec(b)|^(2) , if and only if vec(a) , vec(b) are perpendicular , given vec(a) 1= vec (0) , vec (b) != vec (0)

prove that (vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|^(2)+|vec(b)|^(2) , if and only if vec(a),vec(b) are perpendicular, given vec(a) ne vec(0), vec(b) ne vec(0) .

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

Prove that 2/(b+c)+2/(c+a)+2/(a+b) >0.

Prove that 2/(b+c)+2/(c+a)+2/(a+b) 0.

Prove that : |{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0