**Representation of vector by unit vector or with components**

When a vector is represented graphically, its magnitude is represented by the length of an arrow and its direction is represented by the direction of the arrow. While expressing a vector with components we will consider two cases. e.g. in two dimensions and in three dimensions. Here two dimensional case is discussed below.

**Resolution in two dimensions:** Let OX and OY be the straight lines perpendicular to each other and represent X and Y axes respectively [Figure].

In XY plane the line OP, making an angle θ with X-axis, represents the vector ř both in magnitude and direction. Let consider the co-ordinate of P is (x, y) and in positive X and Y-axes corresponding unit vectors are ȋ and ĵ respectively.

Let the normal PN be drawn from P on X-axis.

Now from figure, we get

ON = x; NP = y and OP = r

so, ON^{→} = xȋ, NP^{→} = yĵ ; and OP^{→} = ř

From the triangle rule,

OP^{→} = ON^{→} + NP^{→}

or, **ř = ȋ + ĵ**

Modulus of this vector,

From figure, we get;

OP^{2} = ON^{2} + NP^{2}

or, r^{2} = i^{2} + y^{2}

then, **r = √( i ^{2} + y^{2})**