A) collinear
B) coplanar
C) non-coplanar
D) non-collinear
E) non-collinear and non-coplanar
Correct Answer: B
Solution :
Equation of plane through the point A (4, 5,1) is \[a(x-4)+b(y-5)+c(z-1)=0\] ...(i) Let points\[B(0,-1,-1)\]and C (3, 9, 4) lies on equation (i), if \[a(0-4)+b(-1-5)+c(-1-1)=0\] \[\Rightarrow \] \[2a+3b+c=0\] ...(ii) and \[-a+4b+3c=0\] ...(iii) On solving Eqs. (ii) and (iii), we get \[\frac{a}{5}=\frac{b}{-7}=\frac{c}{11}\] \[\therefore \]\[5(x-4)-7(y-5)+11(z-1)=0\] \[\Rightarrow \]\[5x-7y+11z+4=0\] is the plane through A, B and C. Now,\[D(-4,4,4)\]lies on it, if \[-20-28+44+4=0\]which is true. \[\therefore \]Points A, B, C and D are coplanar.
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