The position vectors of A and B are vec{a} = | vedclass

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(B) The position vector of the midpoint $M$ of a line segment joining points with position vectors $\vec{a}$ and $\vec{b}$ is given by the formula: $\

Vedclass · Accepted Answer

$2\hat{i} - \hat{j} + \frac{5}{2}\hat{k}$

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(B) The position vector of the midpoint $M$ of a line segment joining points with position vectors $\vec{a}$ and $\vec{b}$ is given by the formula: $\vec{m} = \frac{\vec{a} + \vec{b}}{2}$.Given $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$ and $\vec{b} = 3\hat{i} - \hat{j} + 3\hat{k}$.Adding the vectors: $\vec{a} + \vec{b} = (1+3)\hat{i} + (-1-1)\hat{j} + (2+3)\hat{k} = 4\hat{i} - 2\hat{j} + 5\hat{k}$.Dividing by $2$: $\vec{m} = \frac{4\hat{i} - 2\hat{j} + 5\hat{k}}{2} = 2\hat{i} - \hat{j} + \frac{5}{2}\hat{k}$.Thus,the correct option is $B$.

The position vectors of $A$ and $B$ are $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$ and $\vec{b} = 3\hat{i} - \hat{j} + 3\hat{k}$. The position vector of the midpoint of the line segment $AB$ is:

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