If A, B, C have position vectors (2, 0, 0), (0, 1, 0) and (0, 0, 2). Show that `DeltaABC` is isosceles.

(0,2) . (0,2) = (0,4)

Particles of masses 10 g and 20 g have position vectors (5,3,0) and (2,0,3) respectively. The position vector of their centre of mass is ………… cm.

In DeltaABC the mid points of the sides AB, BC and CA are (l, 0, 0), (0, m, 0) and (0, 0,n) respectively. Then, (AB^2+BC^2+CA^2)/(l^2+m^2+n^2) is equal to

The position vectors of the four angular points of a tetrahedron OABC are (0, 0, 0), (0, 0, 2), (0, 4, 0) and (6, 0, 0) , respectively. A point P inside the tetrahedron is at the same distance 'r' from the four plane faces of the tetrahedron. Then, the value of 9r is.....

If the coordinates (x, y, z) of the point S which is equidistant from the points O(0, 0, 0), A(n^(5), 0, 0), B(0, n^(4), 0), C(0, 0, n) obey the relation 2(x+y+z)+1=0 . If ninZ , then |n|= _____( |*| is the mudulus function).

Show that the points A(1,3,2),B(-2,0,1) and C(4,6,3) are collinear.

If A=[{:(1,0,1),(0,1,2),(0,0,4):}] then show that [3A]=27[A]

Show that the triangle ABC with vertices A(0, 4, 1), B(2, 3, -1) and C(4, 5, 0) is right angled.

The medians AD and BE of the triangle with vertices A(0, b), B(0, 0) and C(a, 0) are mutually perpendicular if

The matrix A=[{:(1,0,0),(0,2,0),(0,0,4):}] is a .......