Consider a cube of side 'a' unit has one vertex at the origin O.
Show that the angle between the main diagonals of the above cube is `cos^-1(1/3)`

Consider a cube of side 'a' unit has one vertex at the origin O. Write down the co-ordinate O, O' , A and A'

Consider a cube of side 'a' unit has one vertex at the origin O. Find the direction ratios of OO' and AA' .

OABCDEFG is acube with edges of length 8 units and axes are shown. L,M,N are midpoints of the edges FG, GD, GB respectively. Show that the angle between the main diagonis is theta=cos^-1(1/3)

An element crystallises' into a, structare which may be described by a cubic type of unit celt having one atom on each C0rner of the cube and two atoms on one of its diagonals. If yolume of this unit cell is 24x 10^-(24) cm^3 and density of element is 7.2 g / cm^-3 . calculate the number of atoms present in 200 g of the element .

An equilateral triangle is inscribed in the parabola y^2 =4ax whose one vertex is at the vertex of the parabola if 1 cms is the side of the equilateral triangle prove that the length of each altitude of the triangle is (1sqrt3)/2 cms

Consider the points A(2,2,-1), B(3,4,2) and C(7,0,6). Find the vector and Cartesian equation of the plane passing these three points. Find the angle between the above plane and the line barr=(i+2j-k)+lambda(i-j+k)

If veca + vecb + vecc = 0, |veca| = 3, |vecb| = 5 and |vecc| = 7, then the angle between veca and vecb is : a) pi/3 b) pi/2 c) cos ^(-1) (( 2)/(225)) d) (pi)/(4)