Prove that `(vec a +vecb).(vec a -vec b)`= `|a|^2+ |b|^2<=> vec a_|_vecb`

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 perpendicular.

Prove that |vec a + vec b| = sqrt (|vec a|^2 + |vec b|^2 + 2 vec a * vec b) .

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

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

For any two vectors vec a and vec b , prove that | vec a xx vec b|^(2) = |vec a|^(2)|vec b|^(2) - (vec a . vecb)^(2) = [[veca.veca veca .vecb], [veca.vecb vec b.vecb]]

For any two vectors vec a and vec b , prove that: | vec a+ vec b|^2=| vec a|^2+| vec b|^2+2 vec adot vec b , | vec a- vec b|^2=| vec a|^2+| vec b|^2-2 vec adot vec b , | vec a+ vec b|^2+| vec a- vec b|^2=2(| vec a|^2+| vec b|^2) and | vec a+ vec b|^2=| vec a- vec b|^2 iff vec a_|_ vec bdot Interpret the result geometrically.

For any two vectors vec a and vec b ,prove that (vec a xxvec b)^(2)=|vec a|^(2)|vec b|^(2)-(vec a*vec b)^(2)

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)

Incase of each of the following statements, state whether it is true or false : For any two non-zero vectors vec a and vec b , (vec a- vecb)^2 = (vec a)^2 +(vec b)^2 - 2vec a*vec b