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In a pentagon ABCDE, show that bar"AB" + bar"AE" + bar"BC" + bar"DC" + bar"ED" = 2bar"AC" - Mathematics and Statistics

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Question

In a pentagon ABCDE, show that `bar"AB" + bar"AE" + bar"BC" + bar"DC" + bar"ED" = 2bar"AC"`

Sum

Solution

LHS = `bar"AB" + bar"AE" + bar"BC" + bar"DC" + bar"ED"`

`= (bar"AB" + bar"BC") + (bar"AE" + bar"ED" + bar"DC")`

`= bar"AC" + bar"AC"`

`= 2bar"AC"` = RHS

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Representation of Vector
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Chapter 5: Vectors - Miscellaneous exercise 5 [Page 190]

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