The component of vector A = 2î + 3ĵ along

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The component of vector $A = 2\hat i + 3\hat j$ along the vector $\hat i + \hat j$is

A

$\frac{5}{{\sqrt 2 }}$

B

$10\sqrt 2 $

C

$5\sqrt 2 $

D

$5$

The component of vector $A = 2\hat i + 3\hat j$ along the vector $\hat i + \hat j$is

$\frac{{\overrightarrow A .\overrightarrow B }}{{|\vec i + \vec j|}} = \frac{{(2\hat i + 3\hat j)\,(\hat i + \hat j)}}{{\sqrt 2 }}$$ = \frac{{2 + 3}}{{\sqrt 2 }} = \frac{5}{{\sqrt 2 }}$