## Resolution of Vectors – Class 11 | Chapter – 4 | Physics Short Notes Series PDF for NEET & JEE

Resolution of Vectors: The resolution of vectors refers to the process of breaking down a vector into its components along two or more perpendicular directions. The components of a vector are the projections of the vector onto these directions, and they can be added or subtracted to obtain the original vector.

## Types of Resolution of Vectors

There are two common types of resolution of vectors in physics: rectangular or Cartesian resolution and polar resolution.

• Rectangular or Cartesian Resolution: In rectangular resolution, a vector is resolved into two or three components along the x, y, and z axes of a Cartesian coordinate system. The x, y, and z components of a vector are obtained by taking the projections of the vector onto the corresponding axes. For example, if v is a vector in three dimensions, then its x-component, vx, is given by the projection of v onto the x-axis. Similarly, the y-component, vy, is given by the projection of v onto the y-axis, and the z-component, vz, is given by the projection of v onto the z-axis.
• Polar Resolution: In polar resolution, a vector is resolved into two components along two perpendicular directions, usually denoted as r and θ. The r-component of the vector is the magnitude of the vector, while the θ-component is the angle that the vector makes with respect to a reference direction. Polar resolution is often used when dealing with circular motion, where the r-component represents the radial distance from the center of the circle, and the θ-component represents the angle of rotation.

## Components of Resolution of Vectors

To find the components of a vector, we typically use trigonometry and the Pythagorean theorem. Here are the steps involved in resolving a vector into its components:

• Choose a set of perpendicular axes, usually denoted by x, y, and z.
• Determine the angle that the vector makes with each axis, usually denoted by θ, φ, and ψ.
• Use trigonometry to find the projections of the vector along each axis. For example, if the vector makes an angle θ with the x-axis and has a magnitude of |v|, then its x-component, vx, is given by vx = |v|cos(θ).
• Repeat this process for each axis to find the components of the vector along each direction.

In two dimensions, a vector can be resolved into two components, usually denoted by vx and vy. In three dimensions, a vector can be resolved into three components, usually denoted by vx, vy, and vz.

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