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GATE Mechanical 2024 | Question: 17

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​​​​A rigid massless tetrahedron is placed such that vertex $\mathrm{O}$ is at the origin and the other three vertices $\text{A, B}$, and $\text{C}$ lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at $\text{A}$ along $x$-axis and another at point $\mathrm{B}$ along $y$-axis. For the body to be in equilibrium, the third point load acting at point $\mathrm{O}$ must be

  1. along $z$-axis
  2. in $x-y$ plane but not along $x$ or $y$ axis
  3. in $y-z$ plane but not along $y$ or $z$ axis
  4. in $z-x$ plane but not along $z$ or $x$ axis
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