Question

Find the vector equation of the line passing through the point having position vector i + 2j + 3k and perpendicular to vectors i + j + k and 2i - j + k.

Answer 1

The vector perpendicular to the vectors \(\bar{b}\) and \(\bar{c}\) is given by

Since the line is perpendicular to the vector \(\bar{b}\) and \(\bar{c}\), it is parallel to \(\bar{b}\) × \(\bar{c}\). The vector equation of the line passing through A ( ) and parallel to \(\bar{b}\) × \(\bar{c}\) is

\(\bar{r} = \bar{a} + λ(\bar{b} \times \bar{c}),\) where λ is a scalar.

Here, \(\bar{a} = \hat{i} + 2\hat{j} + 3\hat{k}\)

Hence, the vector equation of the required line is