Find a unit vector in the direction of overri | vedclass

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Question

(A) Given the coordinates of $P$ and $Q$ are $(5, 0, 8)$ and $(3, 3, 2)$ respectively.$\overrightarrow{PQ} = \overrightarrow{OQ} - \overrightarrow{OP}

Vedclass · Accepted Answer

$-\frac{2}{7}\hat{i} + \frac{3}{7}\hat{j} - \frac{6}{7}\hat{k}$

Vedclass · Answer

(A) Given the coordinates of $P$ and $Q$ are $(5, 0, 8)$ and $(3, 3, 2)$ respectively.$\overrightarrow{PQ} = \overrightarrow{OQ} - \overrightarrow{OP}$$= (3\hat{i} + 3\hat{j} + 2\hat{k}) - (5\hat{i} + 0\hat{j} + 8\hat{k})$$= (3-5)\hat{i} + (3-0)\hat{j} + (2-8)\hat{k} = -2\hat{i} + 3\hat{j} - 6\hat{k}$The magnitude of $\overrightarrow{PQ}$ is $|\overrightarrow{PQ}| = \sqrt{(-2)^2 + 3^2 + (-6)^2} = \sqrt{4 + 9 + 36} = \sqrt{49} = 7.$The unit vector in the direction of $\overrightarrow{PQ}$ is given by $\hat{PQ} = \frac{\overrightarrow{PQ}}{|\overrightarrow{PQ}|} = \frac{-2\hat{i} + 3\hat{j} - 6\hat{k}}{7} = -\frac{2}{7}\hat{i} + \frac{3}{7}\hat{j} - \frac{6}{7}\hat{k}.$

Find a unit vector in the direction of $\overrightarrow{PQ},$ where $P$ and $Q$ have coordinates $(5, 0, 8)$ and $(3, 3, 2),$ respectively.

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