A) 0
B) 1
C) 2
D) 3
Correct Answer: B
Solution :
[b]: If the planes\[x-cy-bz=0\],\[-cx+y-az=0,\]\[-bx-ay+z=0\]pass through a line, then determinant formed by coefficients of unknowns is equal to zero. \[\Rightarrow \left| \begin{matrix} 1 & -c & -b \\ -c & 1 & -a \\ -b & -a & 1 \\ \end{matrix} \right|=0\] \[\Rightarrow 1(1-{{a}^{2}})+c(-c-ab)-b(ca+b)=0\] \[\Rightarrow 1-{{a}^{2}}-{{c}^{2}}-abc-abc-{{b}^{2}}=0\] \[\Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc-1=0\] \[\Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc=1\]You need to login to perform this action.
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