A) \[-\mathbf{i}+\mathbf{j}+\mathbf{k}\]
B) \[-\mathbf{i}-\mathbf{j}+\mathbf{k}\]
C) \[\mathbf{i}+\mathbf{j}-\mathbf{k}\]
D) None of these
Correct Answer: A
Solution :
Let the position vector of P is \[x\mathbf{i}+y\mathbf{j}+z\mathbf{k},\] then \[\overrightarrow{AB}=\overrightarrow{CP}\Rightarrow \mathbf{j}-\mathbf{i}=x\mathbf{i}+y\mathbf{j}+(z-1)\mathbf{k}\] By comparing the coefficients of \[\mathbf{i},\,\,\mathbf{j}\] and \[\mathbf{k},\]we get \[x=-1,\] \[y=1\,\text{and}\,\text{z--1}=\text{0}\Rightarrow z=1\] Hence required position vector is \[-\mathbf{i}+\mathbf{j}+\mathbf{k}.\]
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