Resolution Of Vectors In Plane and Space

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Resolution Of Vectors In Plane (In Two Dimensions)

The process of splitting a single vector into two or more vectors in different directions which collectively produced the same effect as produced by the single vector alone is known as resolution of vector.

The various vectors into which a single vector is splitted are known as components of vectors.

We know that any vector r can be expressed as a linear combination of two unit vectors i^ and j^ at right angle i.e r = x i^ + y j^

The vectors x i^ and y j^ are called the perpendicular components of r. The scalars x and y are called component part of r in the directions of x-axis and y-axis.

Resolution Of Vectors In Plane (In Two Dimensions)
Resolution Of Vectors In Plane (In Two Dimensions)

Resolution Of A Space Vector (In Three Dimensions)

We can resolve a general vector A into three components along X, Y and Z-axis in three dimensions. Let α, β and γ are the angles between A and the X, Y and Z-axis respectively. Let i^, j^ and k^ be the unit vectors along X, Y and Z Axis respectively.

Resolution Of A Space Vector (In Three Dimensions)
Resolution Of A Space Vector (In Three Dimensions)
Resolution Of A Space Vector (In Three Dimensions)
Resolution Of A Space Vector (In Three Dimensions)

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