Question

If the position vector of a point P is $\overline{r}=x\overline{i}+y\overline{j}+z\overline{k}$. where x, y, z $\in$N and $\overline{\alpha }$ is a vector gives the $\overline{\alpha }=\overline{i}+\overline{j}+\overline{k}$, then the total number of possible positions of point P for which $\overline{r}\cdot \overline{\alpha }=10$.

Answer 1

$\begin{array}{c}\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}x,y,z\in N\\ \overrightarrow{\alpha }=\hat{i}+\hat{j}+\hat{k}\\ \overrightarrow{r}.\overrightarrow{\alpha }=10\\ x+y+z=10\\ No.ofso{l}^n{=}^9{C}_2=36\\ \\ Totalnumberofpossiblepositionare36\end{array}$