The projection of $ \vec{v_1} $ on the vector $ \vec{v_2} $ is given by

$$ \text{Proj}_{\vec{b}}{\vec{a}} = \dfrac{ \vec{a} \cdot \vec{b} }{ \| \vec{a} \|^2 } \vec{b}$$

First we find the dot product and magnitude of vector $ \, \vec{b} $:

$$ \begin{aligned}\vec{a} \cdot \vec{b} &= \frac{ 7 }{ 2 } \\[1 em]\| \vec{b} \| &= \frac{\sqrt{ 101 }}{ 2 } \\[1 em]\end{aligned} $$

Now we can find the projection

$$ \text{Proj}_{\vec{b}}{\vec{a}} = \dfrac{ \frac{ 7 }{ 2 } }{ \left( \frac{\sqrt{ 101 }}{ 2 } \right)^2 } \cdot \vec{b} = \dfrac{ \frac{ 7 }{ 2 } }{ \frac{ 101 }{ 4 } } \cdot \vec{b} = \frac{ 14 }{ 101 } \cdot \left(5,~\dfrac{ 1 }{ 2 }\right) = \left(\dfrac{ 70 }{ 101 },~\dfrac{ 7 }{ 101 }\right) $$

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