expression, noun
wrong direction; unexpected direction
Used when something goes or points in a direction different from what was intended or expected. Often implies a mistake or an unforeseen turn of events.
話があらぬ方向にそれてしまった。
The conversation went off in an unexpected direction.
ボールがあらぬ方向に飛んでいった。
The ball flew off in the wrong direction.
見当違い means 'off the mark' or 'misguided' in a more general sense, while あらぬ方向 specifically refers to a physical or metaphorical direction.
The phrase combines the archaic negative form あらぬ (from ある, 'to be') meaning 'not existing' or 'unexpected', with 方向 ('direction'). The exact historical derivation is uncertain, but it is a fixed expression meaning 'an unintended direction'.