Resolution of a Vector in a Plane

When a vector is resolved into its components or parts along different directions, it is called the resolution of a vector. In a plane, a vector can be resolved into two independent directions.

Explanation

To understand why a vector in a plane can be resolved into two independent directions, let's consider a vector A in a plane.

1. Component along x-axis
The x-axis is one of the independent directions in the plane. We can resolve vector A into its component along the x-axis, denoted as Ax.

2. Component along y-axis
The y-axis is another independent direction in the plane. We can also resolve vector A into its component along the y-axis, denoted as Ay.

Independence of Directions
The x-axis and the y-axis are perpendicular to each other and do not depend on each other. This means that the component of vector A along the x-axis does not affect the component of vector A along the y-axis, and vice versa. Therefore, we can say that the components Ax and Ay are independent of each other.

Number of Independent Directions
Since a vector in a plane can be resolved into its components along the x-axis and the y-axis, which are two independent directions, the number of independent directions in which a vector in a plane can be resolved is 2.

Conclusion
Therefore, the correct answer is option 'A' - a vector in a plane can be resolved into 1 independent direction.