Show that `a.(b xx c)` is equal in magnitude to the volume of the parallelepiped formed on the three vectors , a, b and c.

The volume of a tetrahedron formed by the coterminous edges vec a , vec b ,a n d vec c is 3. Then the volume of the parallelepiped formed by the coterminous edges vec a+ vec b , vec b+ vec ca n d vec c+ vec a is

If atimesb=c, btimesc=a, ctimesa=b . If vectors a, b and c are forming a right handed system, then the volume of tetrahedron formed by vectors 3a-2b+2c, -a-2c and 2a-3b+4c is

If the sum of the roots of ax^2bx +c = 0 is equal to the sum of the squares of their reciprocals, then show that c/a, a/b, b/c are in A.P.

Volume of parallelopiped formed by vectors atimesb, btimesc and ctimesa is 36 sq.units. then the volumn formed by the vector a b and c is

If the vectors 2 hat i-3 hat j , hat i+ hat j- hat ka n d3 hat i- hat k form three concurrent edges of a parallelepiped, then find the volume of the parallelepiped.

If vec a , vec b , and vec c are mutually perpendicular vectors of equal magnitudes, then find the angle between vectors vec a and vec a+ vec b+ vec c dot

If vec a, vec b ,vec c are mutually perpendicular vectors of equal magnitudes, show that the vector vec a+ vec b + vec c is equally inclined to vec a, vec b and vec c .

A parallelepiped is formed by planes drawn parallel to coordinate axes through the points A=(1,2,3) and B=(9,8,5). The volume of that parallelepiped is equal to (in cubic units)

If vec a, vec b and vec c are three non-coplanar unit vectors each inclined with other at an angle of 30^@, then the volume of tetrahedron whose edges are vec a,vec b, vec c is (in cubic units)

Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- vec c=0. If the area of triangle formed by vectors vec a and vec b is A , then what is the value of 4A^2?