Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra2 Marks
Question
Find the direction cosines of the vector $\hat i + 2\hat j + 3\hat k$
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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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