Question

If C is the mid -point of AB and P is any point outside AB, then

$PA with rightwards arrow on top space plus space PB with rightwards arrow on top space equals space 2 PC with rightwards arrow on top$
$PA with rightwards arrow on top space plus space PB with rightwards arrow on top space equals space PC with rightwards arrow on top$
$PA with rightwards arrow on top space plus space PB with rightwards arrow on top space plus space 2 PC with rightwards arrow on top space equals space 0$
$PA with rightwards arrow on top space plus space PB with rightwards arrow on top space plus space PC with rightwards arrow on top space equals space 0$

Solution

PA with rightwards arrow on top space plus space PB with rightwards arrow on top space equals space 2 PC with rightwards arrow on top

PA with rightwards arrow on top space plus AC with rightwards arrow on top space plus CP with rightwards arrow on top space equals space 0 PB with rightwards arrow on top space plus BC with rightwards arrow on top space plus space CP with rightwards arrow on top space equals space 0 Adding comma space we space get PA with rightwards arrow on top plus PB with rightwards arrow on top space plus space AC with rightwards arrow on top space plus space BC with rightwards arrow on top space plus 2 CP with rightwards arrow on top space equals space 0 Since space AC with rightwards arrow on top space equals space minus space BC with rightwards arrow on top & space CP with rightwards arrow on top space equals space minus space PC with rightwards arrow on top rightwards double arrow space PA with rightwards arrow on top space plus PB with rightwards arrow on top space minus 2 PC with rightwards arrow on top space equals space 0 space

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