Question

A point on the line $\overline{r}=2\hat{i}+3\hat{j}+4\hat{k}+t(\hat{i}+\hat{j}+\hat{k})$ is

• A. $(2014,2015,2016)$
• B. $(2013,2015,2017)$
• C. $(2013,2014,2017)$
• D. $Noneofthese$

Answer 1

The correct option is A $(2014,2015,2016)$

Given line is $\overline{r}=2\hat{i}+3\hat{j}+4\hat{k}+t(\hat{i}+\hat{j}+\hat{k})$

$\Rightarrow \overline{r}=(2+t)\hat{i}+(3+t)\hat{j}+(4+t)\hat{k}$

For any value of $t\in x$ , the coordinates of i, j , k axes are consecutive numbers. ( $\because$ 2 + t , 3 + t , 4 + t are consecutive) Hence, from the options, we can see that only option A has consecutive integers i.e. 2014 , 2015 , 2016 which can satisfy the above equations.

Therefore, ( 2014 , 2015 , 2016 ) is a point on the line $\overline{r}$