Find the volume of a parallelopiped having three coterminus vectors of equal magnitude `|veca|` and equal inclination `theta` with each other.

Find the volume of a parallelepiped having three vectors of equal magnitude |vec a| and equal inclination theta with each other.

Statement 1: Let V_(1) be the volume of a parallelopiped ABCDEF having veca, vecb, vecc as three coterminous edges and V_(2) be the volume of the parallelopiped PQRSTU having three coterminous edges as vectors whose magnitudes are equal to the areas of three adjacent faces of the parallelopiped ABCDEF . Then V_(2)=2V_(1)^(2) Statement 2: For any three vectors vec(alpha), vec(beta), vec(gamma) [vec(alpha)xxvec(beta),vec(beta)xxvec(gamma),vec(gamma)xxvec(alpha)]=[(vec(alpha),vec(beta),vec(gamma))]^(2)

Statement 1: If V is the volume of a parallelopiped having three coterminous edges as veca, vecb , and vecc , then the volume of the parallelopiped having three coterminous edges as vec(alpha)=(veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc vec(beta)=(veca.vecb)veca+(vecb.vecb)vecb+(vecb.vecc)vecc vec(gamma)=(veca.vecc)veca+(vecb.vecc)vecb+(vecc.vecc)vecc is V^(3) Statement 2: For any three vectors veca, vecb, vecc |(veca.veca, veca.vecb, veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|=[(veca,vecb, vecc)]^(3)

If V is the volume of the parallelopiped having three coterminus edges as a,b and c,then the volume of the parallelopiped having the edges as alpha=(a.a)a+(a.b)c;beta=(a.b)a+(b.b)b+(b.c)b;gamma=(a.c)a+(b.c)b+(c.

Find the vector of magnitude 9 which is equally inclined to the coordinates axes.

The vector of magnitude 6 which is equally inclined to the co-ordinate axes is

If the volume of a parallelopiped whose three coterminal edges are represented by vectors, then lambda =________.

Let vec(a), vec(b), vec(c ) be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle theta, with the vector vec(a) + vec(b) + vec(c ) . The 36 cos^(2) 2 theta is equal to __________ .

If three concurrent edges of a parallelopiped of volume V represent vectors veca,vecb,vecc then the volume of the parallelopiped whose three concurrent edges are the three concurrent diagonals of the three faces of the given parallelopiped is

Find the volume of the tetrahedron having coterminus edges represented by vectors a=j+k, b=i+k" and "c=i+j .