The GATE Grind

GATE 2016 ME (ME3) โ€“ Question 63

Computer Aided Manufacturing and Automation ยท CAD/CAM and their integration ยท 2 marks ยท Multiple choice

A point P (1, 3, โˆ’5) is translated by 2๐‘– + 3๐‘— โˆ’4๐‘˜ and then rotated counter clockwise by 90ยฐ about the z-axis. The new position of the point is

  1. (โˆ’6, 3, โˆ’9)
  2. (โˆ’6, โˆ’3, โˆ’9)
  3. (6, 3, โˆ’9)
  4. (6, 3, 9)

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Correct answer: (A) (โˆ’6, 3, โˆ’9)

Explanation

First translate(1,3,โˆ’5) by(2,3,โˆ’4), obtaining(3,6,โˆ’9). A positive90ยฐ rotation about z maps(x,y,z) to(โˆ’y,x,z). The final point is **(โˆ’6,3,โˆ’9), A**. Reversing the transformation order would give a different point.