1.1.58 Vector Algebra

Condition: two geometric vectors \ (\ bar {p} \) and \ (\ bar {q} \) are given. Present the vector \ (\ bar {p} \) in the form of the sum of two vectors \ (\ overLine {p_ {1}} \) and \ (\ overLine {p_ {2}} \) such that the vector \ (\ overLine {p_}} \) perpendicular to the vector \ (\ bar {q} \), and vector \ (\ overLine {p_ {2}} \) vector \ (\ bar {q} \) collinear. \ [\ bar {p} (2, -4,12), \ quad \ bar {q} (1, -1, -5) \]