Equation of Plane through Origin
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Q. The equation of the plane passing through the intersection of the planes x+2y+3z+4 = 0 and 4x+3y+2z+1=0 and the origin is
- 3x+2y+z+1=0
- 3x+2y+z=0
- 2x+3y+z=0
- x+y+z=0
Q. Consider the following system of equations :
ax+by+cz=0az+bx+cy=0ay+bz+cx=0
List - I List - II(I)If a+b+c≠0 and (P) Planes meet only at one point(a−b)2+(b−c)2+(c−a)2=0.(II)If a+b+c=0 and (Q) Equations represent the line x=y=z(a−b)2+(b−c)2+(c−a)2≠0(III) If a+b+c≠0 and (R) Equations represent identical planes(a−b)2+(b−c)2+(c−a)2≠0(IV)If a+b+c=0 and (S) The solution of the system represents (a−b)2+(b−c)2+(c−a)2=0 whole of the three dimensional space
Which of the following is the "INCORRECT" option?
ax+by+cz=0az+bx+cy=0ay+bz+cx=0
List - I List - II(I)If a+b+c≠0 and (P) Planes meet only at one point(a−b)2+(b−c)2+(c−a)2=0.(II)If a+b+c=0 and (Q) Equations represent the line x=y=z(a−b)2+(b−c)2+(c−a)2≠0(III) If a+b+c≠0 and (R) Equations represent identical planes(a−b)2+(b−c)2+(c−a)2≠0(IV)If a+b+c=0 and (S) The solution of the system represents (a−b)2+(b−c)2+(c−a)2=0 whole of the three dimensional space
Which of the following is the "INCORRECT" option?
- (IV)→(S)
- (II)→(Q)
- (I)→(S)
- (III)→(P)
