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\newcommand\ds{\displaystyle}
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QUESTION

If \textbf{a}=\textbf{i}+\textbf{j} and
\textbf{b}=\textbf{i}+\textbf{j}+\textbf{k} find the component of
\textbf{b} in the direction of \textbf{a}.

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ANSWER


The component of \textbf{b} in direction of ${\bf a} ={\bf
b.}\hat{\bf a}$

 $\ds=(1,1,1).\frac{(1,1,0)}{\sqrt{2}}
=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}+0
=\frac{2}{\sqrt{2}}=\sqrt{2}$


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