Suppose the line αx−2=−5y−2=2z+2 lies on the plane x+3y−2z+β=0. Then, (α+β) is equal to
Answer: 7
Solutions · 1
Official solution
The line passes through (2,2,−2), which must lie on the plane:
\[2+6+4+\beta=0\implies \beta=-12.\]
The line's direction (α,−5,2) must be perpendicular to the plane's normal (1,3,−2):
\[\alpha-15-4=0\implies\alpha=19.\]
\[\alpha+\beta=19-12=7.\]