question_answer

ABCD is a quadrilateral, P, Q are the mid points of\[\overset{\to }{\mathop{BC}}\,\]and\[\overset{\to }{\mathop{AD}}\,\]then\[\overset{\to }{\mathop{AB}}\,+\overset{\to }{\mathop{DC}}\,\]is equal to:

A)  \[3\overset{\to }{\mathop{QP}}\,\]                                      

B)  \[\overset{\to }{\mathop{QP}}\,\]

C)  \[4\overset{\to }{\mathop{QP}}\,\]                      

D)         \[\frac{\overset{\to }{\mathop{QP}}\,}{2}\]

E)  \[2\overset{\to }{\mathop{QP}}\,\]

Correct Answer: E

Solution :

\[\overset{\to }{\mathop{AB}}\,+\overset{\to }{\mathop{DC}}\,\] \[=\overset{\to }{\mathop{QP}}\,+\overset{\to }{\mathop{QP}}\,=2\overset{\to }{\mathop{QP}}\,\]