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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}}\,


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

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