6. The symmetric form of the equations of the line *x*+*y*–*z* = 1, 2*x*-3*y*+*z* = 2 is :

(a) (*x*/2) = (*y*/3) = (*z*/5)

(b) (*x*/2) = (*y*/3) = (*z*-1/5)

(c) (*x*-1/2) = (*y*/3) = (*z*/5)

(d) (*x*/2) = (*y*/3) = (*z*/5)

7. The lines which intersect the skew lines *y=mx*, *z=c; y=-mx, z=-c* and the x-axis lie on the surface :

(a) *cz=mxy*

(b) *cy=mxz*

(c) *xy=cmz*

(d) None of these

8. A plane meets the coordinate axes in A,B,C such that the centroid of the triangle ABC is the point (*a,a,a*). Then the equation of the plane is *x+y+z=p* where *p* is :

(a) *a*

(b) 3/*a *

(c) *a*/3

(d) 3*a*

9. The line (*x*+1)/2 = (*y*+1)/3 = (*z*+1)/4 meets the plane *x*+2*y*+3*z* = 14, in the point :

(a) (3,-2 ,5)

(b) (3,2,-5 )

(c) (2,0,4 )

(d) (1,2,3)

10. The three planes

4*y*+6*z* = 5;

2*x*+3*y*+5*z* = 5;

6*x*+5*y*+9*z* = 10 :

(a) meet in a point

(b) have a line in common

(c) form a triangular prism

(d) none of these

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