how to find subtraction of vectors

 

Asked by chsimha3 | 28th Aug, 2021, 10:36: AM

Expert Answer:

Let begin mathsize 14px style a with rightwards arrow on top end style and begin mathsize 14px style b with rightwards arrow on top end style are two given vectors that are represented by OA and OB as shown in figure.
To subtract  begin mathsize 14px style b with rightwards arrow on top end style from begin mathsize 14px style a with rightwards arrow on top end style , i.e to get ( begin mathsize 14px style a with rightwards arrow on top end stylebegin mathsize 14px style b with rightwards arrow on top end style ) , we should get - begin mathsize 14px style b with rightwards arrow on top end style by reversing the sighn of begin mathsize 14px style b with rightwards arrow on top end style keeping magnitude same
as shown by OC in figure . Vector  ( begin mathsize 14px style a with rightwards arrow on top end stylebegin mathsize 14px style b with rightwards arrow on top end style )  is determined by adding begin mathsize 14px style a with rightwards arrow on top end style and  -begin mathsize 14px style b with rightwards arrow on top end style .
To add begin mathsize 14px style a with rightwards arrow on top end style and -begin mathsize 14px style b with rightwards arrow on top end style , we complete the parallelogram OCEA .  Diagonal OE represents the vector ( begin mathsize 14px style a with rightwards arrow on top end stylebegin mathsize 14px style b with rightwards arrow on top end style )  .
If vectors are given in component form , then ( begin mathsize 14px style a with rightwards arrow on top end stylebegin mathsize 14px style b with rightwards arrow on top end style )  is obtained as given below
begin mathsize 14px style a with rightwards arrow on top space equals space a subscript x space end subscript i with hat on top space plus a subscript y space j with hat on top space plus space a subscript z space k with hat on top space
end style
begin mathsize 14px style b with rightwards arrow on top space equals space b subscript x space end subscript i with hat on top space plus b subscript y space j with hat on top space plus space b subscript z space k with hat on top space
end style

Answered by Thiyagarajan K | 28th Aug, 2021, 12:54: PM