וַהֲדָ֬רְךָ֨ ׀ צְלַ֬ח רְכַ֗ב עַֽל־דְּבַר־אֱ֭מֶת וְעַנְוָה־צֶ֑דֶק וְתוֹרְךָ֖ נוֹרָא֣וֹת יְמִינֶֽךָ׃
And in thy majesty prosper, ride on, In behalf of truth and meekness and righteousness; And let thy right hand teach thee tremendous things.
Rashi on Psalms
for the sake of truth To instruct according to the law and to behave with righteous humility.
Rashi on Psalms
and it shall instruct you The Torah and the matter of truth in which you shall engage shall teach you tactics of war so that your right should perform awesome things. Since he mentions the study of Torah in an expression of war, the expression of the right hand, prepared to fight, is appropriate (i.e., it is customary to fight with the right hand).