# LinAlg4.1.6

If $\bar{a}\,$ is the position vector whose point is $(3,-2)\,$.Find the coordinates of a point B such that $\bar{AB}=\bar{a}\,$,the coordinates of A are $(-1,5)\,$

Let O be the origin and P be the point of $\bar{a}\,$

Then,$\bar{a}=\bar{OP}=3\bar{i}-2\bar{j}\,$

Given $A=-\bar{i}+5\bar{j}\,$ let $B(x,y)\,$

$\bar{AB}=\bar{B}-\bar{A}=(x+1)\bar{i}+(y-5)\bar{j}\,$

Also given $\bar{AB}=\bar{a}=(a+1)\bar{i}+(y-5)\bar{j}=3\bar{i}-2\bar{j}\,$

$x+1=3,y-5=-2,x=2,y=3\,$

Hence$(2,3)\,$ is the required point.

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