If the volume of tetrahedron `A B C D` is 1 cubic units, where `A(0,1,2),B(-1,2,1)a n dC(1,2,1),` then the locus of point `D` is a. `x+y-z=3` b. `y+z=6` c. `y+z=0` d. `y+z=-3`

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a.1 b. 2 c. -1 d. 2

If y+1/z=1 and x+1/y=1 , then what is the value of x y z ? -1 (b) 0 (c) 1/2 (d) 1

The equation of the plane containing the line 2x+z-4=0 nd 2y+z=0 and passing through the point (2,1,-1) is (A) x+y-z=4 (B) x-y-z=2 (C) x+y+z+2=0 (D) x+y+z=2

The equation of the plane containing the line 2x+z-4=0 nd 2y+z=0 and passing through the point (2,1,-1) is (A) x+y-z=4 (B) x-y-z=2 (C) x+y+z+2=0 (D) x+y+z=2

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is 0 b. -1 c. 1 d. 2

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)

A plane through the line (x-1)/1=(y+1)/(-2)=z/1 has the equation (A) x+y+z=0 (B) 3x+2y-z=1 (C) 4x+y-2z=3 (D) 3x+2y+z=0

The values of x,y,z in order of the system of equations 3x+y+2z=3,2x-3y-z=-3,x+2y+z=4, are (A)2,1,5(B)1,1,1(C)1,-2,-1(D)1,2,-1

Equation of plane passing through the points (1,0,1),(1,-1,1) and parallel to the vector hat i+hat j-2k is (A)2x+y+z=3(B)2x+z=3(C)2x-z=3(D)2x-y+z=0