# Find vector equation of a line that passes through a point and is perpendicular to vector

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

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

A vector $\;(a,b,c)\;$ is perpendicular to $\;(1,0,1)\;$ iff
$$(a,b,c)\cdot(1,0,1)=0\iff a+c=0$$
$$(2,1,1)+t(a,b,c)\;,\;\;t\in\Bbb R$$