For any two vectors ` vec a` and `vec b` prove that `( veca dot vecb)^2le| vec a|^2| vec b|^2` and hence show that `(a_1b_2+a_2b_2+a_3b_3)^2lt=(a_1^2+a_2^2+a_3^2)(b_1^2+b_2^2+b_3^2)`

For any two vectors vec a and vec b , prove that (vec a* vec b)^ 2 le |quad vec a|^2|quad vec b|^2 .

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. vec b)^2

For any two vectors vec a and vec b prove that (vec avec b)^(2)<=|vec a|^(2)|vec b|^(2) and hence show that (a_(1)b_(2)+a_(2)b_(2)+a_(3)b_(3))^(2)<=(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(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)

Prove by vector method that (a_1b_1+a_2b_2+a_3b_3)^2lt+(a_1^2+a_2^2+a_3^2)(b_1^2+b_2^2+b_3^2)

For any to vectors vec A and vec B , prove that |vec A xx vec B|^2 = A^2 B^2 - ( vec A. vec B)^2 .

If for any two vectors vec a and vec b , (vec a+ vec b)^2 +(vec a - vecb)^2 =λ {(vec a)^2 +(vec b)^2}, then write the value of λ .

For any two non zero vectors write the value of (| vec a+ vec b|^2+| vec a- vec b|^2)/(| vec a|^2+ | vec b"|^2)

The vectors vec a and vecb are such that |vec a| = 2, |vec b| = 3, veca.vecb = 4 .Find |veca - vec b|

If vec a and vec b are any two vectors, then (vec a xx vec b)^2 +(vec a*vecb)^2 =.......