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Determinant of the matrix formed by the given vectors must be zero, which gives an algebraic equation for a:
R.<a> = PolynomialRing(QQ)
v1=[1,1,3]
v2=[1,0,-2]
v3=[a,3,3]
eq = Matrix([v1,v2,v3]).det()
print(eq.roots(multiplicities=False))
