A tetrahedron has vertices `P(1,2,1),Q(2,1,3),R(-1,1,2) and O(0,0,0)`. The angle beween the faces OPQ and PQR is :

A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), then angle between face O A Ba n dA B C will be a. cos^(-1)((17)/(31)) b. 30^0 c. 90^0 d. cos^(-1)((19)/(35))

P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection length of vec P Qon vec R Sdot

The vertices of trianglePQR are P(0,-4),Q(3,1) and R(-8,1) What is the ratio between the areas of triangleMPN and trianglePQR ?

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. The distance between the orthocenter and the circumcenter of triangle PQR is

Find A^(2)-5A=6I , if A=[(2,0,1),(2,1,3),(1,-1,0)]

The vertices of trianglePQR are P(0,-4),Q(3,1) and R(-8,1) Draw trianglePQR on a graph paper .

For what values of x:[(1,2,1)][(1,2,0),(2,0,1),(1,0,2)][(0),(2),(x)]=O ?

Find the rank of the following matrices. [{:(0,1,2,1),(2,-3,0,-1),(1,1,-1,0):}]

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. Find the value of r