Equation of a Plane : General Form

Q. The projection of the line $\frac{x+1}{-1}=\frac{y}{2}=\frac{z-1}{3}$ on the plane x – 2y + z = 6 is the line of intersection of this plane with the plane

1. 2x + y + 2 = 0
2. 3x + y – z = 2
3. 2x – 3y + 8z = 3
4. 2x - y + 2 = 0

Q. The equation of the plane containing the two lines of intersection of the two pairs of planes x + 2y – z – 3 = 0 and 3x – y + 2z – 1 = 0, 2x – 2y + 3z = 0 and x – y + z + 1 =0 is :

1. 7x – 7y + 8z + 3 = 0
2. 7x – 8y + 9z + 3 = 0
3. 5x – 5y + 6z + 2 = 0
4. None of these

Q.

If the general equation of plane is given by ax + by + cz = d then a, b, c are the direction ratios of the normal to the plane.

1. True

2. False

Q. Reflection of the line $\frac{x-1}{-1}=\frac{y-2}{3}=\frac{z-4}{1}$ in the plane x +y +z =7 is :
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1. $\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-4}{1}$
2. $\frac{x-1}{-3}=\frac{y-2}{-1}=\frac{z-4}{1}$
3. $\frac{x-1}{-3}=\frac{y-2}{1}=\frac{z-4}{-1}$
4. $\frac{x+1}{3}=\frac{y-2}{1}=\frac{z+4}{1}$

Q.

The equation of the plane passing through the points (1, -1, 2) and (2, -2 2) and which is perpendicular to the plane 6x -2y +2z =9 is

1. $x+y-2z+4=0$

2. $x-y-2z=4$

3. $x-2y+z-4=0$

4. $x+2y-z+4=0$