Vector equation of a line given by one fixed coordinate and one linear equation (for example x = 2, 2y - 3z + 7 = 0)

1. A.
   $\vec{r} = (3\hat{i} + 4\hat{k}) + \lambda(2\hat{j} + \frac{5}{3}\hat{k})$
2. B.
   $\vec{r} = (3\hat{i} + 4\hat{k}) + \lambda(2\hat{j} - \frac{5}{3}\hat{k})$
3. C.
   $\vec{r} = 2\hat{j} + \frac{5}{3}\hat{k} + \lambda(3\hat{i} + 4\hat{k})$
4. D.
   $\vec{r} = 2\hat{j} - \frac{5}{3}\hat{k} + \lambda(3\hat{i} + 4\hat{k})$

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1. A.
   $\vec{r} = (2\hat{i} + 2\hat{j} - 3\hat{k}) + \lambda(2\hat{j} - 3\hat{k})$
2. B.
   $\vec{r} = (2\hat{i} + 2\hat{j} - 3\hat{k}) + \lambda(2\hat{i} - 3\hat{j})$
3. C.
   $\vec{r} = \left(2\hat{i} + \dfrac{7}{3}\hat{k}\right) + \lambda(3\hat{j} + 2\hat{k})$
4. D.
   $\vec{r} = \left(-2\hat{i} + \dfrac{7}{3}\hat{k}\right) + \lambda(3\hat{j} + 2\hat{k})$

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