Two balls, having linear momenta $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$, undergo a collision in free space. There is no external force acting on the balls. Let $${\overrightarrow {p'} _1}$$ and $${\overrightarrow {p'} _2}$$ be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of $$p,{a_1},{a_2},{b_1},{b_2},{c_1}$$ and $${c_2}$$ :