If $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c, ¯ ¯ ¯ d$ respectively are the position vectors representing the vertices A, B, C, D of a parallelogram, then write $¯ ¯ ¯ d$ in terms of $¯ ¯ ¯ a, ¯ ¯ b$ and $¯ ¯ c$ .

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Solution

$T a k e A a s n e w o r i g i n o f r e f e r e n c e . W i t h A a s o r i g i n B, C, D c o r r e s p o n d t o v e c t o r s$
$^{'} = \to b - \to a,^{'} = \to c - \to a,^{'} = \to d - \to a r e s p e c t i v e l y .$
$\to$
$B u t t h e r u l e f o r v e c t o r a d d i t i o n w i t h o r i g i n A g i v e s u s t h a t$
$A B C D i s a p a r a l l e l o g r a m i f a n d o n l y i f^{'} =^{'} +^{'} \Rightarrow \to c - \to a = \to b - \to a + \to d - \to a \Rightarrow \to d = \to a + \to c - \to b$

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