If planes x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 pass through a straight line then a2 + b2 + c2 =

Engineering

Mathematics

Introduction to Determinants

Question

If planes x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 pass through a straight line then a² + b² + c² =

1 – abc

abc – 1

1 – 2abc

2abc – 1

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Since, the given planes are concurrent, hence:-

∣ \begin{array}{ccc} 1 & - c & - b \\ c & - 1 & a \\ b & a & - 1 \end{array} ∣ = 0

⇒ 1(1 – a²) + c(– c – ab) – b(ac + b) = 0

⇒ 1 – a² – c² – abc – abc – b² = 0

⇒ a² + b² + c² = 1 – 2abc

Hence, answer is option-(C).

Please subscribe our Youtube channel to unlock this solution.