Resolution and Components of Vectors in a Plane

The process of splitting a vector is called resolution of a vector. In simpler language it would mean, determining the effect of a vector in a particular direction. This is explained with the help of an example later on. The parts of the vector obtained after splitting the vector are known as the components of the vector.

Applying the law of triangle of vectors,

Sub Topics

Rectangular components of a vector
Example of resolution of vector

Rectangular components of a vector

If the components of a given vector are perpendicular to each other, they are called rectangular components. The figure illustrates a vector represented by . Through the point, O two mutually perpendicular axes X and Y are drawn. From the point P, two perpendiculars, PN and PM are dropped on X and Y axes respectively.

of A.

Moreover, in the right-angled DONP, Cosq = A_x / A or A_x = A Cosq --(1)

Squaring and adding 1 and 2,

This equation gives the magnitude of the given vector in terms of the magnitudes of the components of the given vector.

where

Example of resolution of vector

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An example of resolution of a vector is the way a person walks. When a person walks, he/she presses the ground obliquely, (i.e., at an angle to the ground) in the backward direction. The ground offers an equal and opposite reaction in the opposite direction. The vertical component of this reaction balances the weight of the person. The horizontal component helps the person to walk.