If A- B- C- D- E are five points in a plane such that AB - AE - BC - DC - ED - k AC - then the value of k is

Given: nbsp;AB #8594;+AE #8594;+BC #8594;+DC #8594;+ED #8594;=k #160;AC #8594; nbsp; AB #8594;+AE #8594;+BC #8594;+DC #8594;+ED #8 ...

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Byju's Answer

Standard VIII

Mathematics

Axioms

If A, B, C, D...

Question

If A, B, C, D, E are five points in a plane such that $\vec{A B} + \vec{A E} + \vec{B C} + \vec{D C} + \vec{E D} = k \vec{A C},$ then the value of k is _______________.

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Solution

Given: $\vec{A B} + \vec{A E} + \vec{B C} + \vec{D C} + \vec{E D} = k \vec{A C}$

$\vec{A B} + \vec{A E} + \vec{B C} + \vec{D C} + \vec{E D} = k \vec{A C} \Rightarrow (\vec{A B} + \vec{B C}) + \vec{D C} + (\vec{A E} + \vec{E D}) = k \vec{A C} \Rightarrow (\vec{A C}) + \vec{D C} + (\vec{A D}) = k \vec{A C} \Rightarrow (\vec{A C}) + (\vec{A D} + \vec{D C}) = k \vec{A C} \Rightarrow (\vec{A C}) + (\vec{A C}) = k \vec{A C} \Rightarrow 2 (\vec{A C}) = k \vec{A C} \Rightarrow 2 = k$

Hence, the value of k is 2.

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Similar questions

Q. A, B, C, D, E are five coplanar points such that

\vec{D A} + \vec{D B} + \vec{D C} + \vec{A E} + \vec{B E} + \vec{C E} = k \vec{D E,}

then k = ___________________.

Q. A, B, C, D, E are five coplanar points such that

\vec{D A} + \vec{D B} + \vec{D C} + \vec{A E} + \vec{B E} + \vec{C E} = λ \vec{D E}, Then λ =___________________.

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If A, B, C, D, E are five points in a plane such that AB→+AE→+BC→+DC→+ED→=k AC→, then the value of k is _______________.

Given: AB→+AE→+BC→+DC→+ED→=k AC→ AB→+AE→+BC→+DC→+ED→=k AC→⇒AB→+BC→+DC→+AE→+ED→=k AC→⇒AC→+DC→+AD→=k AC→⇒AC→+AD→+DC→=k AC→⇒AC→+AC→=k AC→⇒2AC→=k AC→⇒2=k Hence, the value of k is 2.

If A, B, C, D, E are five points in a plane such that $\vec{A B} + \vec{A E} + \vec{B C} + \vec{D C} + \vec{E D} = k \vec{A C},$ then the value of k is _______________.