Answer:
DC's of the vector \[2\hat{i}-\hat{j}+3\hat{k}.\] are \[\frac{2}{\sqrt{{{(2)}^{2}}+{{(-1)}^{2}}+{{(3)}^{2}}}},\]\[\frac{-1}{\sqrt{{{(2)}^{2}}+{{(-1)}^{2}}+{{(3)}^{2}}}},\] and \[\frac{3}{\sqrt{{{(2)}^{2}}+{{(-1)}^{2}}+{{(3)}^{2}}}},\] \[\left[ \begin{align} & \text{if}\,\,a,b\,\,\text{and}\,\,c\,\,\text{are}\,\,\text{the}\,\,\text{DR }\!\!'\!\!\text{ s,}\,\,\text{then}\,\,\text{DC }\!\!'\!\!\text{ s}\,\,\text{are} \\ & \frac{a}{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}},\frac{b}{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}}\,\text{and}\,\frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}} \\ \end{align} \right]\]\[=\frac{2}{\sqrt{4+1+9}},\] \[\frac{-1}{\sqrt{4+1+9}}\] and \[\frac{3}{\sqrt{4+1+9}}\] \[=\frac{2}{\sqrt{14}},\] \[\frac{-1}{\sqrt{14}}\] and \[\frac{3}{\sqrt{14}}\]
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