\[\overset{\to }{\mathop{a}}\,\text{ },\overset{\to }{\mathop{b}}\,\,\,and\,\,\vec{c}\] are three vectors with magnitude \[|\overset{\to }{\mathop{a}}\,|=4,|\overset{\to }{\mathop{b}}\,|=4,|\overset{\to }{\mathop{c}}\,|=2\] and such that \[\overset{\to }{\mathop{a}}\,\] is perpendicular to is perpendicular to \[(\overset{\to }{\mathop{b}}\,+\overset{\to }{\mathop{c}}\,),\overset{\to }{\mathop{b}}\,\] is perpendicular to \[(\overset{\to }{\mathop{c}}\,+\overset{\to }{\mathop{a}}\,)\] and \[\overset{\to }{\mathop{c}}\,\] is perpendicular to \[(\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,)\]. It follows that \[|\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,+\overset{\to }{\mathop{c}}\,|\] is equal to:

• A. 9
• B. 6
• C. 5
• D. 4