LinAlg4.1.7

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Find a vector of magnitude 6units which is parallel to the vector {\bar  {i}}+{\sqrt  {3}}{\bar  {j}}\,

Let {\bar  {a}}={\bar  {i}}+{\sqrt  {3}}{\bar  {j}}\, then |{\bar  {a}}|={\sqrt  {1+3}}=2\,

Unit vector parallel to {\bar  {a}}\, is {\frac  {1}{2}}({\bar  {i}}+{\sqrt  {3}}{\bar  {j}})\,

Therefore the required vector is 6{\bar  {a}}=6({\frac  {1}{2}}({\bar  {i}}+{\sqrt  {3}}{\bar  {j}})=3{\bar  {i}}+3{\sqrt  {3}}{\bar  {j}}\,

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