Options

A. `{:("(p)",(q),(r),(s)),("(4)",(3),(2),(1)):}`
B. `{:("(p)",(q),(r),(s)),("(2)",(4),(3),(1)):}`
C. `{:("(p)",(q),(r),(s)),("(4)",(3),(1),(2)):}`
D. `{:("(p)",(q),(r),(s)),("(2)",(4),(1),(3)):}`

Answer

A

Explanation

`q. (veca_(k)xxveca_(k+1))=r^(2)sin"" (2pi)/(n)`
`veca_(k).veca_(K+1)=r^(2) cos ""(2pi)/(n)`
`Given |sum _(k-1)^(n-1) veca_(k)xxveca_(k+1)|=|sum_(k=1)^(n-1)a_(k).a_(k+1)|`
`implies r^(2) (n-1)sin ""(2pi)/(n)=r^(2) (n-1) cos"" (2pi)/(n)`
`implies tan ""(2pi)/(n)=1`
`implies tan(2 pi)/(n) =kpi +(pi)/(4),Kin Z`
`implies (8)/(4K+1)`
`implies n=8` ( when=0)
Note :- Solutions of the remaining pats are given in their respective chapters.