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.

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.

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 angle between two lines whose direction ratios are proportional to 1,1,2 and (sqrt(3)-1),(-sqrt(3)-1),4

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.

The direction cosines of a line which is perpendicular to both the lines whose direction ratios are 1,-1,0 and 2,-1,1 are

Prove that the points whose coordinates are respectively (5,1),(1,-1) and (11,4) lie on a straight line and find its intercepts on the axes

The line joining the points (-2,1,-8 and (a,b,c) is parallel to the line whose direction ratios are 6,2, and 3. Find the values of a,b and c

Direction ratios of two lines are a,b,c and 1/bc,1/ca,1/ab. Then the lines are

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