Find a vector of magnitude 11 in the directio | vedclass

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Question

(A) The vector $\overrightarrow{PQ}$ with initial point $P(1,3,2)$ and terminal point $Q(-1,0,8)$ is given by $\overrightarrow{PQ} = (-1-1)\hat{i} + (

Vedclass · Accepted Answer

$\frac{22}{7} \hat{i} + \frac{33}{7} \hat{j} - \frac{66}{7} \hat{k}$

Vedclass · Answer

(A) The vector $\overrightarrow{PQ}$ with initial point $P(1,3,2)$ and terminal point $Q(-1,0,8)$ is given by $\overrightarrow{PQ} = (-1-1)\hat{i} + (0-3)\hat{j} + (8-2)\hat{k} = -2\hat{i} - 3\hat{j} + 6\hat{k}$.The direction opposite to $\overrightarrow{PQ}$ is the direction of $\overrightarrow{QP}$.$\overrightarrow{QP} = -\overrightarrow{PQ} = 2\hat{i} + 3\hat{j} - 6\hat{k}$.The magnitude of $\overrightarrow{QP}$ is $|\overrightarrow{QP}| = \sqrt{2^2 + 3^2 + (-6)^2} = \sqrt{4 + 9 + 36} = \sqrt{49} = 7$.The unit vector in the direction of $\overrightarrow{QP}$ is $\widehat{QP} = \frac{\overrightarrow{QP}}{|\overrightarrow{QP}|} = \frac{2\hat{i} + 3\hat{j} - 6\hat{k}}{7}$.The required vector of magnitude $11$ in the direction of $\overrightarrow{QP}$ is $11 	imes \widehat{QP} = 11 \left( \frac{2\hat{i} + 3\hat{j} - 6\hat{k}}{7} ight) = \frac{22}{7}\hat{i} + \frac{33}{7}\hat{j} - \frac{66}{7}\hat{k}$.

Find a vector of magnitude $11$ in the direction opposite to that of $\overrightarrow{PQ}$,where $P$ and $Q$ are the points $(1,3,2)$ and $(-1,0,8)$ respectively.

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