Question

The following forces are acting on a particle: (1) \( 2i + 3j - 2k \), (2) \( 3i + j + 3k \), and (3) \( -5i + 2j + k \). Now the particle will move in

• A. XY plane
• B. YZ plane
• C. XZ plane
• D. along X-axis

Hint:

For a particle to move in a particular direction, the components of the resultant force must have a non-zero component along that direction.

Answer 1

The Correct Option is D

Step 1: Understanding the forces.
The forces acting on the particle are given in vector form. The resultant force \( F \) is the vector sum of all three forces. Let’s calculate the components of the resultant force: \[ F = (2i + 3j - 2k) + (3i + j + 3k) + (-5i + 2j + k) \] \[ F = (2 + 3 - 5)i + (3 + 1 + 2)j + (-2 + 3 + 1)k = 0i + 6j + 2k \] Step 2: Analyzing the motion.
The resultant force has no component along the x-axis (i.e., \( F_x = 0 \)), so the motion of the particle is along the YZ-plane. However, the resultant force does have components along the y- and z-axes, which causes motion along the YZ plane. Step 3: Conclusion.
The correct answer is (4) along the X-axis.