Discussion
A straight line passes through the points (10,8, 6) and (13,9, 4) . A unit vector parallel to this line is
Answer: E
A unit vector is \(\frac{1}{\sqrt{14}}(3\hat{i} + \hat{j} - 2\hat{k})\).
The direction is the difference of the two points:
\[ \begin{aligned} \vec{d} &= (13 - 10,\ 9 - 8,\ 4 - 6) = (3, 1, -2) \\ |\vec{d}| &= \sqrt{9 + 1 + 4} = \sqrt{14} \end{aligned} \]
Dividing by \(\sqrt{14}\) gives the answer. The option with \(+2\hat{k}\) has the sign of the \(z\)-change wrong, and the \(\sqrt{17}\) options are not unit vectors (\(9 + 1 + 4 = 14\), not 17).
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