Question

Find the vector equation of the line passing through the point having position vector -i - j + 2k and parallel to the line r = (i + 2j + 3k) + λ(3i + 2j + k).

Answer 1

Let A be point having position vector \(\bar{a} = -\hat{i} - \hat{j} + 2\hat{k}\)

The required line is parallel to the line

∴ it is parallel to the vector

\(\bar{b} = 3\hat{i} + 2\hat{j} + \hat{k}\)

The vector equation of the line passing through A(\(\bar{a}\)) and parallel to \(\bar{b}\) is \(\bar{r} = \bar{a} + λ\bar{b}\) where λ is a scalar.

∴ the required vector equation of the line is