A plane is parallel to two lines whose direction ratios are (1,0,-1) and (-1,1,0) and it contains the point (1,1,1).If it cuts coordinate axes at A,B,C then find the volume of the tetrahedron OABC.

Find angle between the two lines whose direction ratios are 1,-2,1 and 4,3,2 respectively

A plane passes through the point (1,1,1) and is parallel to the vectors vec b = (1, 0, - 1) and vec c =(-1,1,0) . If pi meets the axes in A, B, and C, find the volume of the tetrahedron OABC.

If the plane x/2+y/3+z/4=1 cuts the coordinate axes in A, B,C, then the area of triangle ABC is

The plane x/a+y/b+z/c=1 meets the coordinate axes at A,B and C respectively. Find the equation of the sphere OABC.

The plane x/a+y/b+z/c=1 meets the coordinate axes at A,B and C respectively. Find the equation of the sphere OABC.

Find the angles at which a line with direction ratios 2,-1,2 is inclined to each of the coordinate axes.

Find the equation of a plane passing through (1, 1, 1) and parallel to the lines L_1 and L_2 direction ratios (1, 0,-1) and (1,-1, 0) respectively. Find the volume of the tetrahedron formed by origin and the points where this plane intersects the coordinate axes.

Find the equation of a plane passing through (1, 1, 1) and parallel to the lines L_1 and L_2 direction ratios (1, 0,-1) and (1,-1, 0) respectively. Find the volume of the tetrahedron formed by origin and the points where this plane intersects the coordinate axes.

Two vectros vecA and vecB are obtained by joining the origin to the points whose coordinates are (1,0,-1) and (-1,1,1). Find the magnitude of the vectors vecAxxvecB and the direction cosines of this vector.

The centroid of a triangle ABC is at the point (1,1,1). If the coordinates of A and B are (3,-5,7) and (-1,7,-6) respectively, find the coordinates of the point C.