If the position vectors of points A, B, C are | vedclass

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(A) Given the position vectors of points $A, B, C$ are $\vec{a} = \hat{i}$,$\vec{b} = \hat{j}$,and $\vec{c} = \hat{k}$.The vector $\vec{AB}$ is given

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

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(A) Given the position vectors of points $A, B, C$ are $\vec{a} = \hat{i}$,$\vec{b} = \hat{j}$,and $\vec{c} = \hat{k}$.The vector $\vec{AB}$ is given by $\vec{b} - \vec{a} = \hat{j} - \hat{i}$.Let the position vector of point $X$ be $\vec{x}$. Then $\vec{CX} = \vec{x} - \vec{c} = \vec{x} - \hat{k}$.Given $\vec{AB} = \vec{CX}$,we have $\hat{j} - \hat{i} = \vec{x} - \hat{k}$.Therefore,$\vec{x} = -\hat{i} + \hat{j} + \hat{k}$.

If the position vectors of points $A, B, C$ are respectively $\hat{i}, \hat{j}, \hat{k}$ and $\vec{AB} = \vec{CX}$,then the position vector of point $X$ is:

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