Question

Which of the following does not represent a straight line?

• A. $ax+by+cz+d=0,ax+b^{\prime }y+cz+d=0(b\ne b^{\prime })$
• B. $ax+by+cz+d=0,a^{\prime }x+by+cz+d=0(a\ne a^{\prime })$
• C. $ax+by+cz+d=0,ax+by+cz+d^{\prime }=0(d\ne d^{\prime })$
• D. $ax+by+cz+d=0,ax+by+c^{\prime }z+d=0(c\ne c^{\prime })$

Answer 1

The correct option is C $ax+by+cz+d=0,ax+by+cz+d^{\prime }=0(d\ne d^{\prime })$

A. $ax+by+cz+d=0,ax+b^{\prime }y+cz+d=0(b\ne b^{\prime })$
Both the planes are different and are not parallel so they will definitely intersect on a line. Thus option A represents a line.
Similarly B and D represents a line.
But C does not represents line. since $ax+by+cz+d=0,ax+by+cz+d^{\prime }=0(d\ne d^{\prime })$ represents two parallel planes which never intersects.
Hence, option 'C' is correct choice.