Prove that the shortest distance between the diagonals of a rectangular parallelopiped whose coterminous sides are a, b, c and the edges not meeting it are

The shortest distance between a diagonal of a unit cube and the edge skew to it, is

The shortest distance of the point (a, b, c) from y-axis is

Statement 1: Let veca, vecb, vecc be three coterminous edges of a parallelopiped of volume V . Let V_(1) be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then V_(1)=2V . Statement 2: For any three vectors, vecp, vecq, vecr [(vecp+vecq, vecq+vecr,vecr+vecp)]=2[(vecp,vecq,vecr)]

Find the volume of the parallelopiped, whose three coterminous edges are represented by the vectors hati+hatj+hatk,hati-hatj+hatk,hati+2hatj-hatk .

Let veca, vecb, vecc be three unit vectors such that veca. vecb=veca.vecc=0 , If the angle between vecb and vecc is (pi)/3 then the volume of the parallelopiped whose three coterminous edges are veca, vecb, vecc is

The lengths of two opposite edges of a tetrahedron are a and b ; the shortest distane between these edges is d , and the angel between them is theta Prove using vectors that the volume of the tetrahedron is (a b dsi ntheta)/6 .

The length of two opposite edges of a tetrahedron are 12 and 15 units and the shortest distance between them is 10 units. If the volume of the tetrahedron is 200 cubic units, then the angle between the 2 edges is

Find the equations to the diagonals of the rectangle the equations of whose sides are x=a ,x=a^(prime),y=b a n d y=b^(prime)

Prove that the shortest distance between any two opposite edges of a tetrahedron formed by the planes y+z=0, x+z=0, x+y=0, x+y+z=sqrt(3)a is sqrt(2)a .

Angle between diagonals of a parallelogram whose side are represented by veca=2hati+hatj+hatk and vecb=hati-hatj-hatk