Answer
(a) $x+y+z=c$
This is the family of the planes that have normal vectors parallel to $ \lt 1,1,1\gt$. The distance from the plane to the origin varies by changing the value of $c$.
(b) $x+y+cz=1$
This is the family of the planes that intercepts the $xy$-plane at the 2D line $x+y=1$. The distance from the plane to the By varying the value of $c$ makes the plane rotate around the line.
(c) $y cos \theta+zsin \theta=1$
Because there is no $x$, the planes will generates will be parallel to $x-$ axis.
These lines are basically tangent lines to a circle of radius $1$
So, the planes are the tangent lines to a circle of radius $1$ on $yz$ plane extended in the directions parallel to the $x-axis$.
Work Step by Step
(a) $x+y+z=c$
This is the family of the planes that have normal vectors parallel to $ \lt 1,1,1\gt$. The distance from the plane to the origin varies by changing the value of $c$.
(b) $x+y+cz=1$
This is the family of the planes that intercepts the $xy$-plane at the 2D line $x+y=1$. The distance from the plane to the By varying the value of $c$ makes the plane rotate around the line.
(c) $y cos \theta+zsin \theta=1$
Because there is no $x$, the planes will generates will be parallel to $x-$ axis.
These lines are basically tangent lines to a circle of radius $1$
So, the planes are the tangent lines to a circle of radius $1$ on $yz$ plane extended in the directions parallel to the $x-axis$.