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The helicity density matrix elements rho[00] of rho(770)+- and omega(782)mesons produced in Z decays have been measured using the OPAL detector at LEP.Over the measured meson energy range, the values are compatible with 1/3,corresponding to a statistical mix of helicity -1, 0 and +1 states. For thehighest accessible scaled energy range 0.3 < x_E < 0.6, the measured rho[00]values of the rho(770)+- and the omega are 0.373 +- 0.052 and 0.142 +- 0.114,respectively. These results are compared to measurements of other vectormesons.Comment: 21 pages, LaTeX, including 8 eps figures, submitted to European  Physical Journal

A study of spin alignment of $\rho(770)^{\pm}$ and $\omega(782)$ mesons in hadronic Z $^0$ decays