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

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(A) Let the position vector of point $P$ be $\vec{p} = xi + yj + zk.$Given that the position vectors of $A, B, C$ are $\vec{a} = i, \vec{b} = j, \vec{

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$-i + j + k$

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(A) Let the position vector of point $P$ be $\vec{p} = xi + yj + zk.$Given that the position vectors of $A, B, C$ are $\vec{a} = i, \vec{b} = j, \vec{c} = k.$The vector $\overrightarrow{AB} = \vec{b} - \vec{a} = j - i.$The vector $\overrightarrow{CP} = \vec{p} - \vec{c} = xi + yj + (z - 1)k.$Given $\overrightarrow{AB} = \overrightarrow{CP},$ we have $j - i = xi + yj + (z - 1)k.$By comparing the coefficients of $i, j,$ and $k$ on both sides,we get:$x = -1, y = 1, z - 1 = 0 \Rightarrow z = 1.$Thus,the position vector of $P$ is $-i + j + k.$

If the position vectors of the points $A, B, C$ are $i, j, k$ respectively and $P$ is a point such that $\overrightarrow{AB} = \overrightarrow{CP},$ then the position vector of $P$ is

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