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GATE 2022 CE (CE1) – Question 36

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 2 marks · Multiple choice

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis are

  1. $(1,0,\sqrt2)$
  2. $(1,0,-\sqrt2)$
  3. $(-1,0,\sqrt2)$
  4. $(-1,0,-\sqrt2)$

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Show answer and explanation

Correct answer: (A) $(1,0,\sqrt2)$

Explanation

This is a rotation of the **axes**, so use the inverse coordinate transformation. For the stated clockwise x-axis rotation, $y\prime=y\cos45^\circ-z\sin45^\circ=0$, while $z\prime=y\sin45^\circ+z\cos45^\circ=\sqrt2$.

The x coordinate remains 1. **Answer: $(1,0,\sqrt2)$ (A)**.