If the position vectors of the points A and B | vedclass

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

Vedclass · Accepted Answer

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

Vedclass · Answer

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

If the position vectors of the points $A$ and $B$ are $\vec{a} = \hat{i} + 3\hat{j} - \hat{k}$ and $\vec{b} = 3\hat{i} - \hat{j} - 3\hat{k}$,then what will be the position vector of the midpoint of $AB$?

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