12th Class
Mathematics
Sample Paper
Maths Olympiad Model Test Paper-11
question_answer
Let \[\overrightarrow{a}\text{ =}\hat{i}+\hat{j}+\hat{k}\] and \[\overrightarrow{r}\] be a variable vector such that \[\overrightarrow{r}.\,\,\hat{i},\]\[\overrightarrow{r}.\,\,\hat{j},\] and \[\overrightarrow{r}.\,\,\hat{k}\] are positive integers. If \[\overrightarrow{r}.\,\,\overrightarrow{a}\le 12,\] then the total number of such vectors is _________.