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

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

A triangular facet in a $$CAD$$ model has vertices: $${P_1}\left( {0,0,0} \right);\,\,{P_2}\left( {1,1,0} \right)$$ and $$\,{P_3}\left( {1,1,1} \right).$$ The area of the facet is

For the $$CNC$$ part programming, match Group A with Group B: