A) \[{{z}_{1}}+{{z}_{2}}-{{z}_{3}}\]
B) \[{{z}_{1}}-{{z}_{2}}+{{z}_{3}}\]
C) \[{{z}_{2}}+{{z}_{3}}-{{z}_{1}}\]
D) All the above
Correct Answer: D
Solution :
Let \[A,B,C\] be the points represented by the numbers \[{{z}_{1}},{{z}_{2}},{{z}_{3}}\]and P be the point represented by \[z\] Now the four points \[A,B,C,P\] form a parallelogram in the following three orders. (i) \[A,B,P,C\](ii) \[B,C,P,A\]and (iii) \[C,A,P,B\] In case (i), the condition for \[A,B,P,C\]to form a parallelogram is \[\overrightarrow{AB}=\overrightarrow{CP}\] i.e., \[{{z}_{2}}-{{z}_{1}}=z-{{z}_{3}}\] or \[z={{z}_{2}}+{{z}_{3}}-{{z}_{1}}\] Similarly in case (ii) and (iii), the required points \[\overrightarrow{BC}=\overrightarrow{AP}\]or \[{{z}_{3}}-{{z}_{2}}=z-{{z}_{1}}\]i.e., \[z={{z}_{3}}+{{z}_{1}}-{{z}_{2}}\] and \[\overrightarrow{CA}=\overrightarrow{BP}\]or \[{{z}_{1}}-{{z}_{3}}=z-{{z}_{2}}\]i.e., \[z={{z}_{1}}+{{z}_{2}}-{{z}_{3}}\]You need to login to perform this action.
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