Find the position vector of the midpoint of t | vedclass

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Question

(A) The position vector of the midpoint $R$ of the line segment joining points $P(2, 3, 4)$ and $Q(4, 1, -2)$ is calculated using the midpoint formula

Vedclass · Accepted Answer

$3\hat{i} + 2\hat{j} + \hat{k}$

Vedclass · Answer

(A) The position vector of the midpoint $R$ of the line segment joining points $P(2, 3, 4)$ and $Q(4, 1, -2)$ is calculated using the midpoint formula: $\overrightarrow{OR} = \frac{\overrightarrow{OP} + \overrightarrow{OQ}}{2}$.Given $\overrightarrow{OP} = 2\hat{i} + 3\hat{j} + 4\hat{k}$ and $\overrightarrow{OQ} = 4\hat{i} + \hat{j} - 2\hat{k}$.Substituting these values:$\overrightarrow{OR} = \frac{(2\hat{i} + 3\hat{j} + 4\hat{k}) + (4\hat{i} + \hat{j} - 2\hat{k})}{2}$Grouping the components:$\overrightarrow{OR} = \frac{(2 + 4)\hat{i} + (3 + 1)\hat{j} + (4 - 2)\hat{k}}{2}$$\overrightarrow{OR} = \frac{6\hat{i} + 4\hat{j} + 2\hat{k}}{2}$$\overrightarrow{OR} = 3\hat{i} + 2\hat{j} + \hat{k}$.

Find the position vector of the midpoint of the vector joining the points $P(2, 3, 4)$ and $Q(4, 1, -2)$.

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