Mathematics

Prove that the line $$\overline { r }=(2,3,4)+k(3,4,5), k\epsilon R$$ is parallel to the plane $$2x+y-2x=3$$


SOLUTION
Given planes equation is $$2{x}+y-2{z}=3$$
$$\vec r=(2,3,4)+k(3,4,5)$$
$$(2,3,4)$$  does not lies on on the plane $$(\because 2(2)+3-2(4)\neq3)$$
d.r's of line is perpendicular to d.r's of plane $$(\because 3(2)+4(1)+5(-2)=0)$$
$$\implies$$ line is parallal to plane
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