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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

The perpendicular distance of the origin from the plane x - 3y + 4z = 6 is ______ - Mathematics and Statistics

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प्रश्न

The perpendicular distance of the origin from the plane x − 3y + 4z = 6 is ______ 

पर्याय

  • 6

  • `6/sqrt(26)`

  • 36

  • `1/sqrt(26)`

MCQ
रिकाम्या जागा भरा
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उत्तर

`6/sqrt(26)`

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पाठ 1.6: Line and Plane - Multiple choice questions

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

In the given cases, find the distance of each of the given points from the corresponding given plane.

Point                    Plane
(0, 0, 0)           3x – 4y + 12 z = 3


In the given cases, find the distance of each of the given points from the corresponding given plane

Point                   Plane

(3, – 2, 1)             2x – y + 2z + 3 = 0


In the given cases, find the distance of each of the given points from the corresponding given plane.

Point              Plane

(– 6, 0, 0)        2x – 3y + 6z – 2 = 0


Show that the points (1, –1, 3) and (3, 4, 3) are equidistant from the plane 5x + 2y – 7z + 8 = 0


Find the distance of the point  \[2 \hat{i} - \hat{j} - 4 \hat{k}\]  from the plane  \[\vec{r} \cdot \left( 3 \hat{i}  - 4 \hat{j}  + 12 \hat{k}  \right) - 9 = 0 .\]


Find the distance of the point (2, 3, −5) from the plane x + 2y − 2z − 9 = 0.

 

Find the equations of the planes parallel to the plane x + 2y − 2z + 8 = 0 that are at a distance of 2 units from the point (2, 1, 1).

 

Show that the points (1, 1, 1) and (−3, 0, 1) are equidistant from the plane 3x + 4y − 12z + 13 = 0.

 

Find the distance of the point (2, 3, 5) from the xy - plane.

 

Find the distance of the point (3, 3, 3) from the plane \[\vec{r} \cdot \left( 5 \hat{i}  + 2 \hat{j}  - 7k \right) + 9 = 0\]

 

If the product of the distances of the point (1, 1, 1) from the origin and the plane x − y + z+ λ = 0 be 5, find the value of λ.


Find an equation for the set of all points that are equidistant from the planes 3x − 4y + 12z = 6 and 4x + 3z = 7.

 

Find the distance between the point (7, 2, 4) and the plane determined by the points A(2, 5, −3), B(−2, −3, 5) and C (5, 3, −3). 


Find the distance of the point (1, -2, 4) from plane passing throuhg the point (1, 2, 2) and perpendicular of the planes x - y + 2z = 3 and 2x - 2y + z + 12 = 0 


Find the distance between the parallel planes 2x − y + 3z − 4 = 0 and 6x − 3y + 9z + 13 = 0.


Find the equation of the plane which passes through the point (3, 4, −1) and is parallel to the plane 2x − 3y + 5z + 7 = 0. Also, find the distance between the two planes.

 

Find the distance between the planes \[\vec{r} \cdot \left( \hat{i}  + 2 \hat{j}  + 3 \hat{k}  \right) + 7 = 0 \text{ and } \vec{r} \cdot \left( 2 \hat{i}  + 4 \hat{j}  + 6 \hat{k}  \right) + 7 = 0 .\]

 

Find the distance of the point `4hat"i" - 3hat"j" + hat"k"` from the plane `bar"r".(2hat"i" + 3hat"j" - 6hat"k")` = 21.


Find the distance of the point (1, 1 –1) from the plane 3x +4y – 12z + 20 = 0.


Solve the following :

Find the distance of the point (13, 13, – 13) from the plane 3x + 4y – 12z = 0.


The equations of planes parallel to the plane x + 2y + 2z + 8 = 0, which are at a distance of 2 units from the point (1, 1, 2) are ________.


If the foot of perpendicular drawn from the origin to the plane is (3, 2, 1), then the equation of plane is ____________.


Find the distance of the point whose position vector is `(2hat"i" + hat"j" - hat"k")` from the plane `vec"r" * (hat"i" - 2hat"j" + 4hat"k")` = 9


Find the distance of the point (– 2, 4, – 5) from the line `(x + 3)/3 = (y - 4)/5 = (z + 8)/6`


The distance of a point P(a, b, c) from x-axis is ______.


Distance of the point (α, β, γ) from y-axis is ____________.


The distance of the plane `vec"r" *(2/7hat"i" + 3/4hat"j" - 6/7hat"k")` = 1 from the origin is ______.


Find the equation of the plane passing through the point (1, 1, 1) and is perpendicular to the line `("x" - 1)/3 = ("y" - 2)/0 = ("z" - 3)/4`. Also, find the distance of this plane from the origin.


Find the foot of the perpendicular from the point (1, 2, 0) upon the plane x – 3y + 2z = 9. Hence, find the distance of the point (1, 2, 0) from the given plane.


The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are


The equations of motion of a rocket are:
x = 2t,y = –4t, z = 4t, where the time t is given in seconds, and the coordinates of a ‘moving point in km. What is the path of the rocket? At what distances will the rocket be from the starting point O(0, 0, 0) and from the following line in 10 seconds? `vecr = 20hati - 10hatj + 40hatk + μ(10hati - 20hatj + 10hatk)`


Find the distance of the point (2, 3, 4) measured along the line `(x - 4)/3 = (y + 5)/6 = (z + 1)/2` from the plane 3x + 2y + 2z + 5 = 0.


If the distance of the point (1, 1, 1) from the plane x – y + z + λ = 0 is `5/sqrt(3)`, find the value(s) of λ.


Find the coordinates of points on line `x/1 = (y - 1)/2 = (z + 1)/2` which are at a distance of `sqrt(11)` units from origin.


The distance of the point `2hati + hatj - hatk` from the plane `vecr.(hati - 2hatj + 4hatk)` = 9 will be ______.


Find the equations of the planes parallel to the plane x – 2y + 2z – 4 = 0 which is a unit distance from the point (1, 2, 3).


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