Step 1 :Given the polar equations $r \cos \theta=3$ and $r=-7$, we are to convert these to rectangular form.
Step 2 :The polar coordinates (r, θ) can be converted to rectangular coordinates (x, y) using the equations: x = r cos θ and y = r sin θ.
Step 3 :For the first equation, we substitute r cos θ with x to get the rectangular form. Thus, the rectangular form of the equation $r \cos \theta=3$ is $x = 3$.
Step 4 :For the second equation, r = -7, we substitute r with sqrt(x^2 + y^2) to get the rectangular form. Thus, the rectangular form of the equation $r=-7$ is $x^2 + y^2 = 49$.
Step 5 :\(\boxed{x = 3}\) is the rectangular form of the equation $r \cos \theta=3$.
Step 6 :\(\boxed{x^2 + y^2 = 49}\) is the rectangular form of the equation $r=-7$.