# Adding vectors by components

Two vector can be easily summed by using vector sum by geometrical method but it is not practical way to add vectors.

For a simpler and more practical way of adding two or more vectors then we can use component method of vector sum or add vectors by components.

Let there be three vector $\overrightarrow{a}$ , $\overrightarrow{b}$ and $\overrightarrow{s}$

and if vector $\overrightarrow{s}$ is the sum of vectors $\overrightarrow{a}$ and $\overrightarrow{s}$ or ,

$\overrightarrow{s} = \overrightarrow{a} + \overrightarrow{b}$

then,

The x component of vector r is the sum of x components of vector a and b , the y component of vector r is the sum of y components of vector a and b and the z component of vector r is the sum of z components of vector a and b.

Or ,

$r_x = a_x + b_x$

,

$r_y = a_y + b_y$

and

$r_z = a_z + b_z$

Or , $\overrightarrow{r} = ( a_x + b_x) \hat{i} + ( a_y + b_y) \hat{j} + ( a_z + b_z) \hat{k}$

The procedure for adding vector by components also applies to vector subtraction.

For example if :

$\overrightarrow{s} = \overrightarrow{a} - \overrightarrow{b}$

then:

$\overrightarrow{r} = ( a_x - b_x) \hat{i} + ( a_y - b_y) \hat{j} + ( a_z - b_z) \hat{k}$

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