Circular arc on a part profile is being machined on a vertical $$CNC$$ milling machine. $$CNC$$ part program using metric units with absolute dimensions is listed below:

$$\eqalign{ & N60\,\,\,\,G01\,\,\,\,X\,30\,\,\,\,Y\,55\,\,\,\,Z\,5\,\,\,\,F50 \cr & N70\,\,\,\,G02\,\,\,X\,50\,\,\,\,Y\,35\,\,\,\,R\,20 \cr & N80\,\,\,\,G01\,\,\,\,Z\,5 \cr} $$

The coordinates of the center of the circular arc are:

A point $$P\left( {1,\,\,\,3,\,\,\, - 5} \right)$$ is translated by $$2\widehat i + 3\widehat j - 4\widehat k$$ and then rotated counter clockwise by $${90^ \circ }$$ about the $$z$$-axis. The new position of the point is

The figure below represents a triangle $$PQR$$ with initial coordinates of the vertices as $$P(1,3),$$ $$Q(4,5)$$ and $$R(5,3.5).$$ The triangle is rotated in the $$X-Y$$ plane about the vertex $$P$$ by angle in clockwise direction. If sin $$\theta = 0.6$$ and cos $$\theta = 0.8$$, the new coordinates of the vertex $$Q$$ are

In a $$CNC$$ milling operation, the tool has to machine the circular arc from point $$(20, 20)$$ to $$(10, 10)$$ at sequence number $$5$$ of the $$CNC$$ part program. If the center of the arc is at $$(20, 10)$$ and the machine has incremental mode of defining position coordinates, the correct tool path command is