The vector equation of the line joining the points i - 2j + k and -2j +3k is

Question

The vector equation of the line joining the points $\mathbf{i}-2 \mathbf{j}+\mathbf{k}$ and $-2 \mathbf{j}+3 \mathbf{k}$ is

(a) $\mathbf{r}=t(\mathbf{i}+\mathbf{j}+\mathbf{k})$

(b) $\mathbf{r}=t_1(\mathbf{i}-2 \mathbf{j}+\mathbf{k})+t_2(3 \mathbf{k}-2 \mathbf{j})$

(c) $\mathbf{r}=(\mathbf{i}-2 \mathbf{j}+\mathbf{k})+t(2 \mathbf{k}-\mathbf{i})$

(d) $\mathbf{r}=t(2 \mathbf{k}-\mathbf{i})$

Answer 1

Vector equation of a line is

$\begin{aligned}\mathbf{r} & =(\mathbf{i}-2 \mathbf{j}+\mathbf{k})+t(-2 \mathbf{j}+3 \mathbf{k}-(\mathbf{i}-2 \mathbf{j}+\mathbf{k})) \\& =(\mathbf{i}-2 \mathbf{j}+\mathbf{k})+t(-\mathbf{i}+2 \mathbf{k})\end{aligned}$

So, The correct option of this question will be (C).