Introduction:
A vector is a quantity that has both magnitude and direction. It can be represented graphically as an arrow, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction of the vector.

Resolution of a vector:
The resolution of a vector refers to the process of breaking down a vector into its components along different directions. This can be done by using trigonometry and the concept of right triangles.

Independent directions:
When a vector is resolved along independent directions, it means that the vector is broken down into components along directions that are perpendicular or independent of each other. These independent directions are typically represented by mutually perpendicular axes, such as the x, y, and z axes in three-dimensional space.

Explanation of option D:
Option D states that a vector can be resolved along independent directions, which is the correct statement. This means that a vector can be broken down into components along different perpendicular axes. Let's consider a two-dimensional example to illustrate this concept.

Example:
Suppose we have a vector V that is represented by an arrow pointing in a certain direction. We can choose two perpendicular axes, such as the x-axis and the y-axis, to resolve this vector. By using trigonometry, we can determine the components of the vector along these axes.

If the angle between the vector and the positive x-axis is θ, the x-component of the vector can be calculated as Vx = V * cos(θ), and the y-component of the vector can be calculated as Vy = V * sin(θ). Therefore, the vector V can be resolved into two components Vx and Vy along the x and y axes, respectively.

Similarly, in three-dimensional space, a vector can be resolved into three components along the x, y, and z axes. This concept of resolving vectors along independent directions is fundamental in physics and engineering, as it allows us to analyze and solve problems involving forces, velocities, and displacements in multiple dimensions.

Conclusion:
In conclusion, a vector can indeed be resolved along independent directions. This means that a vector can be broken down into components along mutually perpendicular axes, such as the x, y, and z axes in three-dimensional space. Resolving vectors along independent directions is a useful tool in physics and engineering, as it allows us to analyze and solve problems involving vectors in multiple dimensions.