Question

How to derive that a vector can be resolved into rectangular components?

Answer 1

Answer:

See below.

Step-by-step explanation:

So, by parallelogram law of vector addition, if ABCD represents a parallologram such that its sides represent vectors, then,

AB + BC = BD --( 1 )

Here, BD is the resultant vector of the summation of AB and BC.

Let i and j be the unit vectors along the X and the Y axis.

Now, we can take vectors AB and BC such that we can represent them using the unit vectors i and j.

Since i and j have a magnitude of 1, then,

AB = |AB| × i

AB = |AB| × iBC = |BC| × j

Substituting the above values in ( 1 ), we get,

BD = |AB| i + |BC| j

The above representation is the components of vector BD. Suppose, the values for |AB| and |BC| are 3 and 2 then,

BD = 3 i + 2 j