" 6.For any vector "bar(a)" prove that "|vec a timeshat u|^(2)+|vec a timeshat jmath|^(2)+|vec a timeshat k|^(2)=2|vec a|^(2)

For any vector vec a, prove that |vec a xxhat i|^(2)+|vec a xxhat j|^(2)+|vec a xxhat k|^(2)=2|vec a|^(2)

For any vector vec a , prove that | vec axx hat i|^2+| vec axx hat j|^2+| vec axx hat k|^2=2| vec a|^2

Prove that for any vector vec(a) , |vec(a)xx hati|^(2)+|vec(a)xx hatj|^(2)+|vec(a)xx hatk|^(2)=2|vec(a)|^(2) .

For any vector vec a , prove that hat i xx (vec a xx hat i)+ hat j xx (vec a xx hat j) + hat k xx(vec a xx hat k)= 2 vec a

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)

For any vector vec(a) , the value of |vec(a) xx hat(i)|^(2) + |vec(a) xx hat(j)|^(2) + |vec(a) xx hat(k)|^(2) is equal to

Show that for any vector vec(a) , ( vec(a) xx hat(i)) ^(2) + ( vec(a) xx hat(j))^(2) + (vec(a) xx hat(k))^(2) =2 |vec(a) |^(2)

For any three vectors vec a,vec b,vec c, prove that |vec a+vec b+vec c|^(2)=|vec a|^(2)+|vec b|^(2)+|vec c|^(2)+2(vec adot b+vec bvec c+vec c+vec a)

For any vector vec(a), |vec(a)xx hat(i)|^(2)+ |vec(a)xx hat(j)|^(2)+ |vec(a) xx hat(k)|^(2) is equal to

For any two vectors vec u and vec v prove that (vec udot v)^(2)+|vec u xxvec v|^(2)=|vec u|^(2)|vec v|^(2)