Equation of a Plane Parallel to a Given Plane

Q.

What is the equation of a plane?

Q.

Which of the following is parallel to plane 3x - 3y +4z = 7?

1. 3x - 3y +4z = 1

2. 4x - 3y +4z = 7

3. 3x - 4y +4z = 7

4. None of these

Q. The equation of the plane which is parallel to the plane x-2y+2z=5 and whose distance from the point (1, 2, 3) is 1, is

1. x-2y+2z=3
2. x-2y+2z+3=0
3. x-2y+2z=6
4. x-2y+2z+6=0

Q. What is slope and how is it related to calculus?

Q. A point $P$ moves on a plane $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$ and $O$ be the origin. A plane through $P$ and perpendicular to $OP$ meets the coordinate axes at $A,B$ and $C$ respectively. Let $G$ be the centroid of the triangle $ABC$. If the planes through $A,B$ and $C$ parallel to the planes $x=0,y=0$ and $z=0$, respectively, intersect at $Q$, then

1. If $OA=OB=OC$, then $OG=\frac{1}{3}OP$
2. Locus of $Q$ is
   $\frac{1}{ax}+\frac{1}{by}+\frac{1}{cz}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}$
3. Locus of $Q$ is
   $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}$
4. If $OA=OB=OC$, then $OG=OP$

Q. Q.1. Find the value of k so that the straight line 2x + 3y + 4 + k(6x - y + 12) = 0 is perpendicular to the line 7x + 5y - 4 = 0.

Q. The equations of two given planes are
$a_{1}x+b_{1}y+c_{1}z=d_1{a}_{2}x+b_{2}y+c_{2}z=d_2$
If both the planes are parallel then which of the following is true:

1. $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{d_1}{d_2}$
2. $\frac{a_2}{a_1}=\frac{b_2}{b_1}=\frac{c_2}{c_1}=\frac{d_1}{d_2}$
3. $\frac{a_2}{a_1}=\frac{b_2}{b_1}=\frac{c_2}{c_1}\ne \frac{d_2}{d_1}$
4. None of the above

Q.

Equation of plane which is parallel to XY-plane is

1. x = a ; where a is constant.

2. y = b ; where b is constant.

3. z = c ; where c is constant.

4. (x - a) + (y - b) = c ; where a, b, and c are constants.