Question

The equation of a line passing through $(-1,2,-4)$ and parallel to the straight line $\dfrac{-x-1}{4} = \dfrac{2y+1}{-1} = \dfrac{-z+4}{3}$, is:

• A. $\vec{r} = (-\hat{i} + 2\hat{j} - 4\hat{k}) + t(4\hat{i} + 6\hat{j} - 7\hat{k}), \; t \in \mathbb{R}$
• B. $\vec{r} = (-\hat{i} + 2\hat{j} - 4\hat{k}) + t(3\hat{i} + 5\hat{j} - 2\hat{k}), \; t \in \mathbb{R}$
• C. $\vec{r} = (-\hat{i} + 2\hat{j} - 4\hat{k}) + t(8\hat{i} + \hat{j} + 6\hat{k}), \; t \in \mathbb{R}$
• D. $\vec{r} = (-\hat{i} + 2\hat{j} - 4\hat{k}) + t(7\hat{i} + 6\hat{j} + 6\hat{k}), \; t \in \mathbb{R}$
• E. $\vec{r} = (-\hat{i} + 2\hat{j} - 6\hat{k}) + t(8\hat{i} + \hat{j} + 6\hat{k}), \; t \in \mathbb{R}$

Hint:

Parallel lines have proportional direction ratios.

Answer 1

The Correct Option is C