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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