Beginner Vector Geometry #4

Geometry Level pending

Two vectors m → \overrightarrow{m} and n → \overrightarrow{n} satisfy:

  • m → + n → = ( 2 , 7 ) \overrightarrow{m}+\overrightarrow{n}=(2,~7)

  • m → − n → = ( 4 , − 3 ) \overrightarrow{m}-\overrightarrow{n}=(4,~-3)

Find the value of m → ⋅ n → \overrightarrow{m}\cdot\overrightarrow{n} .

This problem is a part of <Beginner Vector Geometry> series .


The answer is 7.

Boi (보이) by Boi (보이) , 19, South Korea

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1 solution

Boi (보이)
Jul 2, 2017

Add the two equations and you get 2 m → = ( 6 , 4 ) 2\overrightarrow{m}=(6,~4) .

∴ m → = ( 3 , 2 ) \therefore~\overrightarrow{m}=(3,~2) .

Subtract the second equation from the first and you get 2 n → = ( − 2 , 10 ) 2\overrightarrow{n}=(-2,~10) .

∴ n → = ( − 1 , 5 ) \therefore~\overrightarrow{n}=(-1,~5) .

∴ m → ⋅ n → = ( 3 , 2 ) ⋅ ( − 1 , 5 ) = − 3 + 10 = 7 \therefore~\overrightarrow{m}\cdot\overrightarrow{n}=(3,~2)\cdot(-1,~5)=-3+10=7 .

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