Suppose point $$P1$$ in $$APT$$ (Automatically programmed Tool) programming is coded by statement
$$P1 = POINT/XSMALL,\,\,\,INTOF,\,\,\,LN1,\,\,CR1$$

The coded geometric situation without causing error is

A stepper motor has $$150$$ steps. The output shaft of the motor is directly coupled to a lead screw of pitch $$4mm,$$ which drives a table. If the frequency of pulse supply to the motor is $$200Hz$$, the speed of the table (in $$mm/min)$$ is

The geometric transformation specified by

$$\left[ {x'\,\,y'\,\,1} \right] = \left[ {x\,\,y\,\,1} \right]\left[ {\matrix{ {0.5} & 0 & 0 \cr 0 & {0.25} & 0 \cr 1 & 2 & 1 \cr } } \right]$$ in a $$2D.$$
In a $$2D$$ $$CAD$$ system represents................

In a $$CAD$$ package, a point $$P(6, 3, 1)$$ is projected along a vector $$v(-2, 1, -1).$$ The projection of this point on $$X-Y$$ plane will be