Question

The vector equation of the straight line $\frac{x-2}{1} = \frac{y}{-3} = \frac{1-z}{2}$ is:

• A. $\vec{r} = 2\hat{i} + \hat{k} + t(\hat{i} + 3\hat{j} + 2\hat{k})$
• B. $\vec{r} = 2\hat{i} - \hat{k} + t(\hat{i} - 3\hat{j} - 2\hat{k})$
• C. $\vec{r} = 2\hat{i} + \hat{k} + t(\hat{i} - 3\hat{j} + 2\hat{k})$
• D. $\vec{r} = 2\hat{i} - \hat{j} + t(\hat{i} - 3\hat{j} - 2\hat{k})$
• E. $\vec{r} = 2\hat{i} + \hat{k} + t(\hat{i} - 3\hat{j} - 2\hat{k})$

Hint:

Always look at the $z$ term carefully. If it is $k-z$, the direction ratio $n$ in the denominator must be multiplied by $-1$ to get the correct direction vector.

Answer 1

Answer: (E)