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Q.

a¯andb¯form the consecutive sides of a regular hexagon ABCDEF.

 List I List II
(A)If CD¯=xa¯+yb¯,then(P)x=2;y=1
(B)If CE¯=xa¯+yb¯,then(Q)x=2,  yR
(C)If AE¯=xa¯+yb¯,then(R)y=1,  x=1
(D)If AD¯=xb¯,then(S)y=2;x=1
  (T)x=0;  y=2
 (A)(B)(C)(D)
(1)RPQS
(2)RPTS
(3)RPST
(4)RPSQ

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a

1

b

2

c

3

d

4

answer is D.

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Detailed Solution

AB¯=a¯  &BC¯=b¯
Question Image
AC¯=AB¯+BC¯=a¯+b¯
AD¯=2.BC¯=2b¯CD¯=AD¯AC¯=2b¯a¯+b¯=b¯a¯FA¯=CD¯=a¯b¯DE¯=AB¯=a¯;   EF¯=BC¯=b¯AE¯=AD¯+DE¯=2b¯a¯
CE¯=CD¯+DE¯=b¯a¯a¯=b¯2a¯

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