What should be the the angle ` theta` between two vectors `vec A and vec B` for their resultant ` vec R` to be (i) maximum (ii) minimum ? Give their resultant value.

Explanation

Magnitude of ` vec R` is
` R sqrt(A^2 + B^2 AB cos theta)` .
(i) For ` R` to be maximum , ` cos theta = + or theta =0^@`
` R_(max) = sqrt (A^2 + B^2 + 2 AB ) =A + B)`
(ii) For `R` to be minimum,
` cos theta =- 1 or theta =180^@ ` ,
` R_(max) = sqrt (A^2 + B^2 + 2 AB(-1))=(A-B)`.