Equation of a Plane Passing through Three Points

Q.

If four points P (1, 2, 3) , Q (2, 3, 4), R(3, 4, 5), S(4, 5, k) are coplanar then the value of k is / are -

1. 6

2. 4

3. 5

4. Any real number.

Q.

Find the equation of plane passing through the points P (1, 1, 1) , Q (3, -1, 2) and R (-3, 5 , -4).

1. 6x + 16y +16z - 44 = 0

2. x - 2y +16z - 13 = 0

3. 6x + 6y +16z - 28 = 0

4. x + 6y +6z - 22 = 0

Q.

If a plane cuts off intercepts -6, 3, 4 from the co-ordinate axes, then the length of the perpendicular from the origin to the plane is

1. $\frac{1}{\sqrt{61}}$

2. $\frac{13}{\sqrt{61}}$

3. $\frac{12}{\sqrt{29}}$

4. $\frac{5}{\sqrt{41}}$

Q.

Let P be the image of the point (3, 1, 7) with respect to the plane x - y + z = 3. Then, the equation of the plane passing through P and containing the straight line $\frac{x}{1}=\frac{y}{2}=\frac{z}{1}$ is

1. x + y - 3z = 0

2. 3x + z = 0

3. x - 4y + 7z = 0

4. 2x - y = 0

Q. The three lines drawn from O with direction ratios, (1, –1, k), (2, –3, 0) and (1, 0, 3) are coplanar. Then k =

1. 1
2. 0
3. no such k exists
4. 7

Q.

If four points P (1, 2, 3) , Q (2, 3, 4), R(3, 4, 5), S(4, 5, k) are coplanar then the value of k is / are -

1. 6

2. 4

3. 5

4. Any real number.

Q. A variable plane intersects the coordinate axes at $A,B,C$ and is at a constant distance $p$ from $O(0,0,0).$ Then the locus of the centroid of the tetrahedron $OABC$ is

1. $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=16p^2$
2. $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{16}{p^2}$
3. $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2}$
4. $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{4}{p^2}$

Q.

If a plane cuts off intercepts -6, 3, 4 from the co-ordinate axes, then the length of the perpendicular from the origin to the plane is

1. 
   

2. 
   

3. 
   

4. 
   

Q.

Let P be the image of the point (3, 1, 7) with respect to the plane x - y + z = 3. Then, the equation of the plane passing through P and containing the straight line $\frac{x}{1}=\frac{y}{2}=\frac{z}{1}$ is

1. 2x - y = 0

2. x - 4y + 7z = 0

3. x + y - 3z = 0

4. 3x + z = 0

Q. Find the direction ratio of the plane passing through the points
R(2, 5, – 3), S(– 2, – 3, 5) and T(5, 3, – 3).

1. (1, 2, 5)
2. (4, 8, -3)
3. (2, 3, 4)
4. (3, 3, 4)