Transform a plane after finding intersections and parallel offsets

A has position vector $-\mathbf i-11\mathbf j+2\mathbf k$. Line l is $(x-9)/7=y+3=-(z+1)/2$, and plane p is $5x+3y+bz+1=0$.

(i) If l and p meet in exactly one point, what can be said about b?2 marks

Use b=1 for the rest.

(ii) Find N, their intersection.3 marks

(iii) Show the shortest distance from A to p is $\sqrt{35}$.3 marks

(iv) Plane p1 is parallel to p at shortest distance $2\sqrt{35}$. Find a possible equation in scalar-product form.3 marks

(v) Plane p undergoes, in order: translation 3 units in negative x; scaling parallel to the y-axis by factor 1/2; reflection in the xy-plane. Find a Cartesian equation of the resulting p2.3 marks