LinAlg4.1.5

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If {\bar  {OA}}={\bar  {i}}+{\bar  {j}}+{\bar  {k}},{\bar  {AB}}=3{\bar  {i}}+2{\bar  {j}}+{\bar  {k}},{\bar  {BC}}={\bar  {i}}+2{\bar  {j}}-2{\bar  {k}},{\bar  {CD}}=2{\bar  {i}}+{\bar  {j}}+3{\bar  {k}}\,,then find the position vector of D.

{\bar  {OD}}={\bar  {OA}}+{\bar  {AB}}+{\bar  {BC}}+{\bar  {CD}}\,

{\bar  {OD}}=({\bar  {i}}+{\bar  {j}}+{\bar  {k}})+(3{\bar  {i}}+2{\bar  {j}}+{\bar  {k}})+({\bar  {i}}+2{\bar  {j}}-2{\bar  {k}})+2{\bar  {i}}+{\bar  {j}}+3{\bar  {k}})\,

{\bar  {OD}}=7{\bar  {i}}+2{\bar  {j}}+3{\bar  {k}}\,

Therefore,the position vector of D relative to O as origin is 7{\bar  {i}}+2{\bar  {j}}+3{\bar  {k}}\,


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