Practicing Success
If C is the mid point of AB and P is any point outside AB, then |
$\vec{PA}+\vec{PB}+\vec{PC}=\vec 0$ $\vec{PA}+\vec{PB}+2\vec{PC}=\vec 0$ $\vec{PA}+\vec{PB}=\vec{PC}$ $\vec{PA}+\vec{PB}=2\vec{PC}$ |
$\vec{PA}+\vec{PB}=2\vec{PC}$ |
Using triangle law of addition of vectors in triangles PAC and PBC, we have $\vec{PA}+\vec{AC}=\vec{PC}$ and $\vec{PB}+\vec{BC}=\vec{PC}$ $⇒\vec{PA}+\vec{AC}+ \vec{PB}+\vec{BC}=\vec{PC} + \vec{PC}$ $⇒\vec{PA}+\vec{PB}+(\vec{AC}+\vec{BC}) = 2\vec{PC}$ $⇒\vec{PA}+\vec{PB}+(\vec{AC}-\vec{AC})=2\vec{PC}$ $⇒\vec{PA}+\vec{PB}=2\vec{PC}$ |