Let the line
x−23=y−1−5=z+22
lies in the plane x+3y−αz+β=0. Then (α,β) equals
(−6,7)
Dr's of line = (3, -5, 2)
Dr's of normal to the plane = (1, 3, - α )
Line is perpendicular to normal ⇒3(1)−5(3)+2(−α)=0⇒3−15−2α=0⇒2α=−12⇒α=−6
Also (2, 1, -2) lies on the plane
2+3+6(−2)+β=0⇒β=7
∴(α,β)=(−6,7)