For any vectors `a,b,|axxb|^(2)+(a*b)^(2)` is equal to

If a and b are two vectors , then (atimesb)^(2) is equal to

If a=i-j and b=j+k , then |axxb|^(2)+|a.b|^(2) is equal to

For any four vectors a,b,c and d, (axxb)xx(cxxd)=["a c d"]b-["b c d"]a and (axxb)xx(cxxd)=["a b d"]c-["a b c"]d .

Lagrange identity: If vector a;b are any two vectors then |vec axvec b|^(2)=|vec a|^(2)|rarr|^(2)-(vec a*vec b)^(2)

Prove that |axxb|^2=a^2b^2-(a*b)^2 .