[" 2.Let "V" be the volume of the parallelopiped formed "n_(0)" ,"],[" vectors "quad vec a=a_(1)hat i+a_(2)hat j+a_(3)hat k,quad vec b=b_(1)hat i+b_(2)hat j_(1)hat y_(1)],[vec c=c_(1)hat i+c_(2)hat j+c_(3)hat k*" If "a_(r)b_(r)*c_(r)" where "r=1,2,3," are "],[" negative real numbers and "sum_(r=1)^(3)(a_(r)+b_(r)+c_(r))=3L_(r)],[" that "V<=L^(3)]

Let V be the volume of the parallelepiped formed by the vectors vec a=a_(i)hat i+a_(2)hat j+a_(3)hat k and vec b=b_(1)hat i+bhat j+b_(3)hat k and vec c=c_(1)hat i+c_(2)hat j+c_(3)hat k. If a_(r),b_(r) and cr, where r=1,2,3, are non-negative real numbers and sum_(r=1)^(3)(a_(r)+b_(r)+c_(r))=3L show that V<=L^(3)

Let V be the volume of the parallelopiped formed by the vectors vec a = a_1 hat i +a_2 hat j +a_3 hat k and vec b =b_1 hat i +b_2 hat j +b_3 hat k and vec c = c_1 hat i + c_2 hat j + c_3 hat k . If a_r, b_r and c_r , where r = 1, 2, 3, are non-negative real numbers and sum_(r=1)^3(a_r+b_r+c_r)=3L show that V le L^3

Let V be the volume of the parallelepiped formed by the vectors vec a = a_i hat i +a_2 hat j +a_3 hat k and vec b =b_1 hat i +b_2 hat j +b_3 hat k and vec c = c_1 hat i + c_2 hat j + c_3 hat k . If a_r, b_r and c_ r, where r = 1, 2, 3, are non-negative real numbers and sum_(r=1)^3(a_r+b_r+c_r)=3L show that V le L^3

Let V be the volume of the parallelopied formed by the vectors overset(to)(a) =a_(1) hat(i) +a_(2)hat(j) +a_(3)hat(k) , overset(to)(b) =b_(1)hat(i) +b_(2)hat(j) +b_(3)hat(k) " and " overset(to)(C) =c_(1)hat(i) +c_(2)hat(j) +c_(3)hat(k) If a_(r) , b_(r) , c_(r) where r=1,2,3 are non-negative real numbers and overset(3)underset(r=1)(Sigma) (a_(r)+b_(r)+c_(r))=3L. Show that V le L^(3)

vec a=a_(1)hat i+a_(2)hat j+a_(3)hat k;vec b=b_(1)hat i+bhat j+b_(3)hat k,*vec c=c_(1)hat i+c_(2)hat j+c_(3)hat k and [3vec a+vec b3vec b+vec c3vec c+vec a]=28[vec avec bvec c], then find the value of (lambda)/(4)

Let the vectors vec a,vec b,vec c be given as a_(1)hat i+a_(2)hat j+a_(3)hat k,b_(1)hat i+b_(2)hat j+b_(3)hat k,c_(1)hat i+c_(2)hat j+c_(3)hat k. Then show that vec a xx(vec b+vec c)=vec a xxvec b+vec a xxvec c

If vec a=a_1 hat i+a_2 hat j+a_3 hat k ,\ vec b=b_1 hat i+b_2 hat j+b_3 hat k and vec c=c_1 hat i+c_2 hat j+c_3 hat k , then verify that vec axx( vec b+ vec c)= vec axx vec b+ vec axx vec c

If vec a=a_1 hat i+a_2 hat j+a_3 hat k ,\ vec b=b_1 hat i+b_2 hat j+b_3 hat k\ a n d\ vec c=c_1 hat i+c_2 hat j+c_3 hat k , then verify that vec axx( vec b+ vec c)= vec axx vec b+ vec axx vec c

If vec (a) = a_(1) hat (i) + a_(2) hat (j) + a_(3) hat (k) , vec(b) = b_(1) hat (i) + b _(2) hat (j) + b_(3) hat (k) and vec (c ) = c_(1) hat (i) + c_(2) hat (j) + c_(3) hat (k) prove that vec (a ) xx ( vec (b) + vec (c ) ) = vec ( a) xx vec ( b) + vec (a) xx vec(c)

Let the vectors veca, vecb, vec c be given as a_(1)hat i + a_(2)hatj + a_(3)hat k, b_(1)hat i + b_(2) hat j + b_(3) hat k , c_(1)hat i + (c_(2)hat j )+( c_(3)hat k) .Then show tha vec a xx(vec b + vec c) = (vec a xx vec b)+( vec a xx vec c ).