Suppose the line x-2/α = y-2/-5 = z+2/2 lies on the plane x + 3y – 2z + β = 0. Then (α + β) is equal to ____.

Question

Suppose the line

\(\cfrac{x-2}{\alpha}\) = \(\cfrac{y-2}{-5}\) = \(\cfrac{z+2}{2}\) lies on the plane x + 3y – 2z + β = 0. Then (α + β) is equal to ____.

Answer 1

Point (2, 2, –2) also lies on given plane

So 2 + 3 × 2 – 2(–2) +\(\beta\) = 0

\(\Rightarrow\) 2 + 6 + 4 + \(\beta\) = 0

\(\Rightarrow\) \(\beta\) = –12

Also \(\alpha\) × 1 – 5 × 3 + 2 × –2 = 0

\(\Rightarrow\) \(\alpha\) – 15 – 4 = 0 

\(\Rightarrow\) \(\alpha\) = 19

\(\therefore\) \(\alpha\)+\(\beta\) = = 19 – 12 = 7