Question
Find the direction cosines of the vector $\hat i + 2\hat j + 3\hat k$

Answer

Let
$\overrightarrow a =\hat i + 2\hat j + 3\hat k $, Then ,
$\widehat a = \frac{{\overrightarrow a }}{{\left| {\overrightarrow a } \right|}} = \frac{{\widehat i + 2\widehat j + 3\widehat k}}{{\sqrt {{1^2} + {2^2} + {3^2}} }} = \frac{{\widehat i + 2\widehat j + 3\widehat k}}{{\sqrt {14} }}$
Therefore , the D.C.’s of vector a are :
$\frac{1}{{\sqrt {14} }},\;\frac{2}{{\sqrt {14} }},\;\frac{3}{{\sqrt {14} }}.$

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