There are two displacement vectors,, one of magnitude ` 3` metres and the other of `4` metres. How would the two vectors be added so that the magnitude of the resultant vector be (a) 7 metres (b) 1 metre and ( c ) 5 metres.

Explanation

The magnitude of resultant ` vec R` of two vectors ` vec A and vec B` is given by
` R= sqrt(A^2 + B^2 + 2 AB cos theta) ,
wher ` A =3 m and B= 4 m`.
Now, ` R= sqrt(3^2 + 4^2 + 2 xx 3 xxx 4 cos theta)`.
(a) `R` will be ` 7m` if ` theta =0^@` (b) ` R` will be ` 1 ` metre if ` theta =180^@` and (c ) ` R` will be ` 5m` if ` theta =90^2`.