" Prove that "(vec a+vec b)*(vec a-vec b)=a^(2)-b^(2)

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 (vec a + vec b) * (vec a-vec b) = | a | ^ (2) + | b | ^ (2) hArrvec a perpvec b

If vec a and vec b be perpendicular vectors, then prove that (vec a + vec b)^(2) = (vec a - vec b)^(2) .

If vec a and vec b are orthogonal vectors, prove that (vec a + 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.

Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and interpret it geometrically.

Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and interpret it geometrically.

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 .

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])xx(vec a+vec b)=2(vec a xxvec b) and interpret it geometrically.