וַהֲדָ֬רְךָ֨ ׀ צְלַ֬ח רְכַ֗ב עַֽל־דְּבַר־אֱ֭מֶת וְעַנְוָה־צֶ֑דֶק וְתוֹרְךָ֖ נוֹרָא֣וֹת יְמִינֶֽךָ׃
און אין דײַן פּראַכט באַגליק, רײַט אַרױס, פֿון װעגן אמת און מילדקײט און גערעכטיקײט, און זאָל דיר דײַן רעכטע האַנט פֿאָרכטיקס באַװײַזן.
Rashi
for the sake of truth To instruct according to the law and to behave with righteous humility.
Rashi
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).