A tetrahedron has vertices of `O(0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C(-1, 1, 2)`. Then, the angle between the faces OAB and ABC will be

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))

Let A(1, 2, 3), B(0, 0, 1) and C(-1, 1, 1) are the vertices of triangleABC . Q. The area of (triangleABC) is equal to

The volume of a right triangular prism ABCA_1B_1C_1 is equal to 3. If the position vectors of the vertices of thebase ABC are A(1, 0, 1), B(2,0, 0) and C(O, 1, 0) , then position vectors of the vertex A_1 , can be

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

If A,B,C are points (1,0,-1), (0,1,-1) and (-1,0,1) respectively find the sine of the angle between the lines AB and AC.

STATEMENT-1 : The centroid of a tetrahedron with vertices (0, 0,0), (4, 0, 0), (0, -8, 0), (0, 0, 12)is (1, -2, 3). and STATEMENT-2 : The centroid of a triangle with vertices (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_(3), z_(3)) is ((x_(1)+x_(2)+x_(3))/3, (y_(1)+y_(2)+y_(3))/3, (z_(1)+z_(2)+z_(3))/3)

The vertices of a triangle ABC are A(0, 0), B(2, -1) and C(9, 2) , find cos B .

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

Find the angles of /_\ABC whose vertices are A((-1,3,2), B(2,3,5) and C(3,5,-2) .

The volme of a tetrahedron having vertices A(1,1,1),B(1,2,4),C(3,1,-2) and D(4,3,1) is x cubic unit then 2x=