If the planes x – cy – bz = 0, cx – y + az = 0 and bx + ay – z
= 0 pass through a straight line, then find the value of
a 2 + b 2 + c 2 + 2abc.
Text Solution
Verified by Experts0001
Ans. 0001
Sol. Given planes are
x – cy – bz = 0 ... (i)
cx – y + az = 0 ... (ii)
bx + ay – z = 0 ... (iii)
equation of plane passing through the line of intersection of plane (i) and (ii) may be taken as
(x – cy –bz) + λ (cx – y + az) = 0
⇒ (1 + λ c) x – y (c + λ ) + z (a λ – b) = 0 ....(iv)
If plane (iii) and (iv) are same then
= 
= 
⇒ λ = – 
= – 
⇒ a – a 3 + bc – a 2 bc = a 2 bc + ac 2 + ab 2 + bc
⇒ a 2 + b 2 + c 2 + 2abc = 1
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