Consider the given vectors, a×(a×c)+b=0 a×(a×c)=−b [a×(a×c)]2=b2 [(a.c)a−(a.a)c]2=b2 Further simplify the above, [(ac‌cos‌θ)a−a2.c]=b2 [2‌cos‌θ‌a−c]2=b2 4cos2θ.a2+c2−4‌cos‌θ.a.c=1 4cos2θ+4−4cos2θ.1.2=1 Further simplify the above, −4cos2θ=−3 cos2θ=