" Gef Prove that "|vec a timesvec b|=sqrt(a^(2)b^(2)-(vec a*vec b)^(2))" ."

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

Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2) .

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)

Solve (vec a timesvec a)*vec b

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

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

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