Find a unit vector in the direction of $\vec{PQ}$, where $P$ and $Q$ have coordinates $(5, 0, 8)$ and $(3, 3, 2)$, respectively.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $-\frac{2}{7}\hat{i} + \frac{3}{7}\hat{j} - \frac{6}{7}\hat{k}$ ##
Since, the coordinates of $P$ and $Q$ are $(5, 0, 8)$ and $(3, 3, 2)$, respectively.
$∴\vec{PQ} = \vec{OQ} - \vec{OP}$
$= (3\hat{i} + 3\hat{j} + 2\hat{k}) - (5\hat{i} + 0\hat{j} + 8\hat{k})$
$= -2\hat{i} + 3\hat{j} - 6\hat{k}$
$∴$ Unit vector in the direction of $\vec{PQ} = \frac{\vec{PQ}}{|\vec{PQ}|}$
$= \frac{-2\hat{i} + 3\hat{j} - 6\hat{k}}{\sqrt{(-2)^2 + (3)^2 + (-6)^2}}$
$= \frac{-2\hat{i} + 3\hat{j} - 6\hat{k}}{\sqrt{49}} = \frac{-2\hat{i} + 3\hat{j} - 6\hat{k}}{7}$