The correct options are
B (→b×→c)×→a→b.→a
C →a×(→c×→b)→a.→b
→x×→b=→c×→b.... {1}
Pre-multiplying both sides of {1} by →a, we get
→a×(→x×→b)=→a×(→c×→b)
Simplifying the above equation, we get
(→a⋅→b)→x−(→a⋅→x)→b=→a×(→c×→b)
∵→x is perpendicular to →a;→a⋅→x=0
∴→x=→a×(→c×→b)→a⋅→b
Also, →b×→x=→b×→c.... {2}
Post-multiplying both sides of {2} by →a, we get
(→b×→x)×→a=(→b×→c)×→a)
Simplifying the above equation, we get
(→a⋅→b)→x−(→a⋅→x)→b=→a×(→c×→b)
∵→x is perpendicular to →a;→a⋅→x=0
∴→x=(→b×→c)×→a→b⋅→a
Hence, option B,C.