Vector equation of a line given as ax + b = cy + d = ez + f

1. A.
   $\vec{r} = (\hat{i}-\frac{\hat{j}}{3}+\frac{\hat{k}}{3})+\lambda(3\hat{i}+2\hat{j}+\hat{k})$
2. B.
   $\vec{r} = (-\hat{i}+\frac{\hat{j}}{3}-\frac{\hat{k}}{3})+\lambda(\frac{1}{2}\hat{i}+\frac{1}{3}\hat{j}+\frac{1}{6}\hat{k})$
3. C.
   $\vec{r} = (3\hat{i}-\hat{j}-\hat{k})+\lambda(3\hat{i}+2\hat{j}+\hat{k})$
4. D.
   $\vec{r} = (\hat{i}-\hat{j}+\hat{k})+\lambda(\frac{1}{2}\hat{i}+\frac{1}{3}\hat{j}+\frac{1}{6}\hat{k})$

Tap an option to check your answer.

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

Tap an option to check your answer.

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

Tap an option to check your answer.