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Compute the magnitude of the following vectors: $(i)\;\overrightarrow a = \hat i + \hat j + \hat k$

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Toolbox:
• The distance between the initial point and the terminal point of a vector is the magnitude (or length) of the vector $\overrightarrow{AB}$.It is denoted by $\mid\overrightarrow{AB}\mid$ or simply $AB$.
• $\mid\overrightarrow{AB}\mid=\sqrt{a_1^2+a_2^2+a_3^2}$
• Where $\overrightarrow{AB}=a_1\hat i+a_2\hat j+a_3\hat k.$
Step 1:
$\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}$
Here $a_1=1,a_2=1$ and $a_3=1$
$\mid \overrightarrow{a}\mid=\sqrt{a_1^2+a_2^2+a_3^2}$
Step 2:
Hence $\mid\overrightarrow{a}\mid=\sqrt{1^2+1^2+1^2}$
$\qquad\qquad\;=\sqrt{3}$
answered May 16, 2013

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