A vector directed at an angle with the co-ordinate axis, can be resolved into its components along the axes. This process of splitting a vector into its components is known as resolution of a vector.

*Resolution
of vectors and rectangular components*

*A vector
directed at an angle with the co-ordinate axis, can be resolved into its
components along the axes. This process of splitting a vector into its
components is known as resolution of a vector.*

Consider a vector R = Vector( OA) making an angle θ with X - axis. The vector R can be resolved
into two components along X - axis and Y-axis respectively. Draw two
perpendiculars from A to X and Y axes respectively. The intercepts on these
axes are called the scalar components *R _{x}*
and

Then, OP is *R ^{x},*
which is the magnitude of

From ∆ OPA,

cos θ = OP/OA = R_{x}/R
(or) R_{x}=Rcos θ

sin θ = OQ/OA = R_{y}/R
(or) R_{y}=Rsin θ

R2 = R_{x}^{2} + R_{y}^{2}

Also, Vector R can be expressed as Vector R = R_{x}i + R_{y}j
where i and j are unit vectors.

In terms of R_{x} and R_{y} , θ can be expressed as
θ = tan^{−1} [R_{y}/R_{x}]

**Scalar and vector quantities**

A study of motion will involve the introduction
of a variety of quantities, which are used to describe the physical world.
Examples of such quantities are distance, displacement, speed, velocity,
acceleration, mass, momentum, energy, work, power etc. All these quantities can
be divided into two categories ? *scalars*
and *vectors*.

*The scalar quantities have magnitude only. *It is denoted by a* *number and unit. Examples : length, mass, time, speed, work,
energy,

temperature etc. Scalars of the same kind can
be added, subtracted, multiplied or divided by ordinary laws.

*The vector quantities have both magnitude and direction. *Examples:*
*displacement, velocity, acceleration, force, weight, momentum, etc.

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Resolution of vectors and rectangular components |

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