LinAlg4.1.6

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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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