Three Dimensional Geometry Question 102
Question: The planes $ x=cy+bz,y=az+cx,z=bx+ay $ pass through one line, if
Options:
A) $ a+b+c=0 $
B) $ a+b+c=1 $
C) $ a^{2}+b^{2}+c^{2}=1 $
D) $ a^{2}+b^{2}+c^{2}+2abc=1 $
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Answer:
Correct Answer: D
Solution:
The planes are concurrent, therefore $ | ,\begin{matrix} -1 & c & b \\ c & -1 & a \\ b & a & -1 \\ \end{matrix}, |=0,\Rightarrow ,a^{2}+b^{2}+c^{2}+2abc=1 $ .
BETA
