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Find the vector equation of line that passes through $(2,1,1)$ and is perpendicular to vector $d=(1,0,1)$

Any hint on solving this problem? what I have thought of is $(1,0,1)* \text{perpendicular Vector}=0$, but I can't seem to derive it

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  • $\begingroup$ Where is the plane in your question? $\endgroup$
    – DonAntonio
    Feb 24, 2016 at 12:13
  • $\begingroup$ I assume it is vector d instead $\endgroup$
    – user317339
    Feb 24, 2016 at 12:13
  • $\begingroup$ Thank you, but then I think you should change the head of your question. $\endgroup$
    – DonAntonio
    Feb 24, 2016 at 12:14

1 Answer 1

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A vector $\;(a,b,c)\;$ is perpendicular to $\;(1,0,1)\;$ iff

$$(a,b,c)\cdot(1,0,1)=0\iff a+c=0$$

So just choose one such vector and the line you want is simply

$$(2,1,1)+t(a,b,c)\;,\;\;t\in\Bbb R$$

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  • $\begingroup$ is there anyway to derive (a,b,c)? and also what about the zero vector $\endgroup$
    – user317339
    Feb 24, 2016 at 12:16
  • $\begingroup$ @user317339 The zero vector is perpendicular to any other vector, but it doesn't work in this case (check this). As for how to derive the vector: it is written in the answer. $\endgroup$
    – DonAntonio
    Feb 24, 2016 at 12:20
  • $\begingroup$ so, a=1 and c=-1 is alright? thanks! $\endgroup$
    – user317339
    Feb 24, 2016 at 12:21

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