L is the equation of the straight line which passes through the point (2, –1, –1); is parallel to the plane 4x + y + z + 2 = 0 and is perpendicular to the line of intersection of the planes 2x + y = 0 = x – y + z. If the point (3, α , β ) lies on line L, then | α + β | is
Text Solution
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(6)
Sol. 
⇒ 4a + b + c = 0 ...(i)
2x + y = 0 = x – y + z ⇒ 
= 
a – 2b – 3c = 0 ... (ii)
From (i) & (ii)
4a + b + c = 0 ⇒ a – 2b – 3c = 0 ⇒ 
⇒ 
∴ equation of the line
⇒ 
= 
= 
⇒ α = – 14 and β = 8 ⇒ | α + β | = 6.
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