Question

A straight line passes through the point whose position vector is $\hat{k}$. The straight line also passes through the point of intersection of the lines $\vec{r} = \hat{j} + \lambda \hat{i}, \lambda \in \mathbb{R}$ and $\vec{r} = \hat{i} + s\hat{j}, s \in \mathbb{R}$. Then the equation of the straight line is:

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

Hint:

Direction vector of line through two points is their difference.

Answer 1

The Correct Option is A