The equation of the line passing through (−2, 3, 4) and parallel to the vector \(2\hat{\imath} - \hat{\jmath} + \hat{k}\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\vec{r} = (-2\hat{\imath} + 3\hat{\jmath} + 4\hat{k}) + \lambda(2\hat{\imath} - \hat{\jmath} + \hat{k})\)
The vector equation of a line through the point with position vector \(\vec{a}\) and parallel to \(\vec{b}\) is
\(\vec{r} = \vec{a} + \lambda\vec{b}\)
Here the point is (−2, 3, 4) and the line is parallel to \(2\hat{\imath} - \hat{\jmath} + \hat{k}\):
\(\vec{a} = -2\hat{\imath} + 3\hat{\jmath} + 4\hat{k}\)
\(\vec{b} = 2\hat{\imath} - \hat{\jmath} + \hat{k}\)
So
\(\vec{r} = (-2\hat{\imath} + 3\hat{\jmath} + 4\hat{k}) + \lambda(2\hat{\imath} - \hat{\jmath} + \hat{k})\)