Discussion
The vector equation of the straight line \(\frac{x - 2}{3} = \frac{y + 1}{2} = \frac{z - 3}{2}\) is
Answer: B
The vector equation is \((2\hat{i} - \hat{j} + 3\hat{k}) + \mu(3\hat{i} + 2\hat{j} + 2\hat{k})\).
From \(\frac{x - 2}{3} = \frac{y + 1}{2} = \frac{z - 3}{2}\), the line passes through the point \((2, -1, 3)\) and has direction ratios \((3, 2, 2)\). The vector form is \(\vec{r} = \vec{a} + \mu\vec{b}\) with \(\vec{a}\) the point and \(\vec{b}\) the direction.
Option A gets the signs of the point and the direction wrong. Options C, D and E swap the roles of the point and the direction, or alter their components.
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