26. Prove that the points `O(0,0,0), A(2.0,0), B(1,sqrt3,0) and C(1,1/sqrt3,(2sqrt2)/sqrt3)` are the vertices of a regular tetrahedron.,

26. Prove that the points O(0,0,0),A(2.0,0),B(1,sqrt(3),0) and C(1,(1)/(sqrt(3)),(2sqrt(2))/(sqrt(3))) are the vertices of a regular tetrahedron...

Show that the points O(0, 0), A(3, sqrt(3)) "and "B(3, -sqrt(3)) are the vertices of an equilateral triangle. Find the area of this triangle.

If points O(0,0) A(3,sqrt(3)) and B(3,a) are the vertices of an equilaterla triangle then a=

Prove that the tetrahedron with vertices at the points O(0,0,0),A(0,1,1),B(1,0,1) and C(1,1,0) is a regular one.

Four point charges q, -2q, -q and 2q are placed at points (0,0,0) m , (sqrt(2), 0,0) m, (sqrt(2), sqrt(2),0)m " and " (0, sqrt(2) , 0) m respectively . The electric field at point ((1)/(sqrt2), (1)/(sqrt2),0) m " is " (q=1muC)

If the vertices of a triangle are (sqrt5,0) and (sqrt3,sqrt2) , and (2,1) then the orthocentre of the triangle is

Statement 1: Distance of point D( 1,0,-1) from the plane of points A( 1,-2,0) , B ( 3, 1,2) and C( -1,1,-1) is 8/sqrt229 Statement 2: volume of tetrahedron formed by the points A,B, C and D is sqrt229/ 2

If the area of the triangle having vertices (a+1,0)(a-1,0) and (a,sqrt(3)) is k sqrt(3) ,then the value of "K" is