If `|a|=a` and `| vec b|=b ,` prove that `( vec a/(a^2)- vec b/(b^2))^2` = `(( vec a- vec b)/(a b))^2` .

If |vec a|=vec a and |vec b|, prove that ((vec a)/(a^(2))-(vec b)/(b^(2)))^(2)=((vec a-vec b)/(ab))^(2)

If |vec a|=a and |vec b|=b then prove that ((vec a)/(a^(2))-(vec b)/(b^(2)))=((vec a-vec b)/(ab))^(2)

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

Prove that (vec(a)-vec(b)) xx (vec(a) +vec(b))=2(vec(a) xx vec(b))

Prove that (vec a * vec b) ^ (2) <= vec a ^ (2) * vec b ^ (2)

Prove that (vec(a) + vec(b)) xx (vec(a) - vec(b)) = 2 (vec(b) xx vec(a))

Prove that |vec(a) xx vec(b)| = sqrt(a^(2)b^(2) -(vec(a) -vec(b))^(2))

If |vec a|=1=|vec b| and |vec a + vec b|=sqrt3 then evaluate (2 vec a - vec b) * (3 vec a + vec b) .

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

Show that | vec a xxvec b | = sqrt (vec a ^ (2) vec b ^ (2) - (vec a * vec b) ^ (2))