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The position vector of a point P is $\vec{r} = x \vec{i} + y \vec{j} + z \vec{k}$ , where
$x \in N, y \in N, z \in N$ and $\vec{a} = \vec{i} + \vec{j} + \vec{k}$ . If $\vec{r} \cdot \vec{a} = 10$ , the number of possible position of P is

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Detailed Solution

$\vec{r .} \vec{a} = 10 \Rightarrow x + y + z = 10$

Number of positive integral solution of above equation = Coeff. of $x^{10}$ in ${(x + x^{2} + x^{3} + ....)}^{3} = 36$

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