Home
Class 12
MATHS
Let V be the volume of the parallelepipe...

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`

Promotional Banner

Similar Questions

Explore conceptually related problems

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)

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

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i+3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j+2hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i-3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j-2hat k

Find vec a.( vec bxx vec c)\ if\ vec a=2 hat i+ hat j+3 hat k ,\ vec b=- hat i+2 hat j+ hat k\ a n d\ vec c=3 hat i+ hat j+2 hat kdot

If vec A=hat I + 2 hat j -3 hat k , vec B =2 hat I -hat j + hat k and vec Chat I -3 hat j + 2 hat k , then find vec A xx ( vec B xx vec C).

Find the volume of the parallelepiped whose edges are represented by the vectors vec(a)=(2hat(i)-3hat(j)+4hat(k)), vec(b)=(hat(i)+2hat(j)-hat(k)) and vec(c)=(3hat(i)-hat(j)+2hat(k)) .

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot

vec a = a_1 hat i a_2 hat j a_3 hat k |a| = 1 , &, vec a. vec b = 2 vec b = b_1 hat i b_2 hat j b_3 hat k |b| = 4 vec c = 2 (vec a times vec b) - 3 vec b then angel between vec c and vec b

If vec a= hat i+ hat j+ hat k , vec c= hat j- hat k , vec adot vec b=3 and vec ax vec b= vec c , then vec b is equal to