Given :
Vector A has a magnitude of 63 units and points west, while vector B has the same magnitude and points due south.
To Find :
The magnitude and direction of
a) A + B .
b) A - B.
Solution :
Let , direction in north is given by +j and east is given by +i .
So , [tex]A=-63i[/tex] and [tex]B=63j[/tex]
Now , A + B is given by :
[tex]A+B=-63i+63j[/tex]
[tex]| A+B | = 63\sqrt{2}[/tex]
Direction of A+B is 45° north of west .
Also , for A-B :
[tex]A-B=-63i-63j[/tex]
[tex]|A-B|=63\sqrt{2}[/tex]
Direction of A-B is 45° south of west .
( When two vector of same magnitude which are perpendicular to each other are added or subtracted the resultant is always 45° from each of them)
Hence , this is the required solution .
