Question

Find the vector and cartesian equations of the line passing through the point of intersection of the lines \( \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) \) and \( \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) \) and parallel to the line \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).

Hint:

Always ensure the given line equation is transformed into the standard form where the variables \(x\), \(y\), and \(z\) have coefficients of \(+1\) before extracting the direction ratios from the denominators. \nobreak

Answer 1