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
[Math] Find vector equation of a line that passes through a point and is perpendicular to vector
vectors
Best Answer
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
$$(2,1,1)+t(a,b,c)\;,\;\;t\in\Bbb R$$