Two vectors ` vec A and vec B` are added. Prove that the magitude of the resultant v ector can bot be greater than ( A +B) and smaller than (A - B) or (B -A).

Explanation

The magnitude of resultant vector ` vec R` of two vectors ` vec Aand vec B` is given by
` R =sqrt ( A^2 + B^2 + 2 AB cos theta ) `
Case 9i). `R` will be maximum if
` cos theta =1 or theta =180^@`
then ` R =sqrt( A^2 + B^2 + 2 AB (1))`
= `(A = B) or (B -A)`.