Show that the line represented by equation `x=ay+b,z=cy+d` in symmetric form is`(x-b)/a=y/1=(z-d)/c`

The equation of the line x+y+z-1=0 , 4x+y-2z+2=0 written in the symmetrical form is

The equation of the line x+y+z-1=0 , 4x+y-2z+2=0 written in the symmetrical form is

The equation of the line x+y+z-1=0 , 4x+y-2z+2=0 written in the symmetrical form is

The equation of the line x+y+z-1=0 , 4x+y-2z+2=0 written in the symmetrical form is

The two lines x=ay+b,z=cy+d and x=a'y+b', z=c'y +d' are pendicular to each other if

A symmetrical form of the line of intersection of the planes x=ay+b and z=cy+d is

If the planes y=az+cx, x=cy+bz+z=bx+ay meet in a line show that the line of intersection of these planes is x/sqrt(1-a^2)=y/sqrt(1-b^2)=z/sqrt(1-c^2)

The system of equations ax-y- z=a-1 ,x-ay-z=a-1,x-y-az=a-1 has no solution if a is:

the two lines x=ay+b,z=cy+d and x=a\'y+b,z=c\'y+d\' will be perpendicular, if and only if: (A) aa\'+c c' + 1=0 (B) aa\'+b b\'+c c'+1=0 (C) aa\'+b b\'+c c'=0 (D) (a+a\')+(b+b\')+(c+c\')=0

The Cartesian equations of a line are x=a y+b ,z=c y+d Find its direction ratios and reduce it to vector form.