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Mathematics Question on Vector Algebra

If CC is the mid point of ABAB and PP is any point outside ABAB, then :

A

PA→+PB→+PC→=0→\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC} = \overrightarrow{0}

B

PA→+PB→+2PC→=0→\overrightarrow{PA}+\overrightarrow{PB}+2\overrightarrow{PC} = \overrightarrow{0}

C

PA→+PB→=PC→\overrightarrow{PA}+\overrightarrow{PB} = \overrightarrow{PC}

D

PA→+PB→=2PC→\overrightarrow{PA}+\overrightarrow{PB} = 2\overrightarrow{PC}

Answer

PA→+PB→=2PC→\overrightarrow{PA}+\overrightarrow{PB} = 2\overrightarrow{PC}

Explanation

Solution

If CC is mid point of ABAB and PP be the origin, then PC→=PA→+PB→2.\overrightarrow{PC}=\frac{\overrightarrow{PA}+\overrightarrow{PB} }{2}. Let PP be the origin outside of ABAB and CC is mid point of ABAB, then PC→=PA→+PB→2\overrightarrow{PC}=\frac{\overrightarrow{PA}+\overrightarrow{PB} }{2} ⇒2PC→=PA→+PB→\Rightarrow 2\overrightarrow{PC} =\overrightarrow{PA} +\overrightarrow{PB}