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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