If vectors \[\vec{a}\] and \[\vec{b}\] are two adjacent sides of a Parallelogram, then the vector representing the altitude of the parallelogram which is perpendicular to \[\vec{a}\] is

• A. \[\vec{b}+\frac{\vec{b}\times \vec{a}}{{{\left| {\vec{a}} \right|}^{2}}}\]
• B. \[\frac{\vec{a}\cdot \vec{b}}{{{\left| {\vec{b}} \right|}^{2}}}\]
• C. \[\vec{b}-\frac{\vec{b}\cdot \vec{a}}{{{\left| {\vec{a}} \right|}^{2}}}\vec{a}\]
• D. \[\frac{\vec{a}\times (\vec{b}\times \vec{a})}{{{\left| {\vec{b}} \right|}^{2}}}\]