Vectors

|a||b|cos(60⁰)=1
|b|=1

Let r=la+mb+naxb

(la+mb+naxb).a=2
l|a|²+ma.b=2
4l+m=2

also r.b=8
(la+mb+naxb).b=8
la.b+m|b|²=8
l+m=8

solve for l and m
l=-2 m=10

also
(r+2a-10b).(a x b) = 4√3
(-2a+10b+naxb+2a-10b).(axb) = 4√3 ..putting value of l and m

n|(axb)|²=4√3
n(√3)²=4√3
n=4√3/3

λ=4√3/3

none matching... may be some calculation mistake

but i can find no mistake in this.. may be options wrong... :O

i got the same answer you got,thats why i posted here

options are wrong then.. :)