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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Subjective Medium Published on 09th 09, 2020
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