Beginner Vector Geometry #1

Geometry Level 2

Two vectors a → = ( x + 1 , 2 ) \overrightarrow{a}=(x+1,~2) and b → = ( 1 , − x ) \overrightarrow{b}=(1,~-x) are perpendicular to each other.

Find the value of real number x x .

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


The answer is 1.

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

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1 solution

Boi (보이)
Jul 1, 2017

Two vectors are perpendicular, therefore:

2 x + 1 ⋅ − x 1 = − 1 \dfrac{2}{x+1}\cdot\dfrac{-x}{1}=-1

2 x = x + 1 2x=x+1

∴ x = 1 \therefore~\boxed{x=1}

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