हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • 6

  • `6/sqrt(26)`

  • 36

  • `1/sqrt(26)`

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

`6/sqrt(26)`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.6: Line and Plane - Multiple choice questions

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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 a point (2, 5, −3) from the plane `vec r.(6hati-3hatj+2 hatk)=4`


Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x − y + z = 0. Also find the distance of the plane, obtained above, from the origin.


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 (1, 2, –1) from the plane x - 2y + 4z - 10 = 0 .


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


Show that the points \[\hat{i}  - \hat{j}  + 3 \hat{k}  \text{ and }  3 \hat{i}  + 3 \hat{j}  + 3 \hat{k} \] are equidistant from the plane \[\vec{r} \cdot \left( 5 \hat{i}  + 2 \hat{j}  - 7 \hat{k}  \right) + 9 = 0 .\]

  

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 \[\vec{r} \cdot \left( 5 \hat{i}  + 2 \hat{j}  - 7k \right) + 9 = 0\]

 

Find the distance of the point (1, −2, 3) from the plane x − y + z = 5 measured parallel to the line whose direction cosines are proportional to 2, 3, −6.


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 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 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.

 

The distance between the planes 2x + 2y − z + 2 = 0 and 4x + 4y − 2z + 5 = 0 is 

 

 

 

 
 

The image of the point (1, 3, 4) in the plane 2x − y + z + 3 = 0 is


The distance of the line \[\vec{r} = 2 \hat{i} - 2 \hat{j} + 3 \hat{k} + \lambda\left( \hat{i} - \hat{j}+ 4 \hat{k}  \right)\]  from the plane \[\vec{r} \cdot \left( \hat{i} + 5 \hat{j} + \hat{k} \right) = 5\] is

 


If a plane passes through the point (1, 1, 1) and is perpendicular to the line \[\frac{x - 1}{3} = \frac{y - 1}{0} = \frac{z - 1}{4}\] then its perpendicular distance from the origin is ______.


Write the coordinates of the point which is the reflection of the point (α, β,  γ) in the XZ-plane.


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 `3hat"i" + 3hat"j" + hat"k"` from the plane `bar"r".(2hat"i" + 3hat"j" + 6hat"k")` = 21.


Solve the following :

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


The equation of the plane passing through (3, 1, 2) and making equal intercepts on the coordinate axes 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 coordinates of the point where the line through (3, – 4, – 5) and (2, –3, 1) crosses the plane passing through three points (2, 2, 1), (3, 0, 1) and (4, –1, 0)


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


Find the distance of a point (2, 4, –1) from the line `(x + 5)/1 = (y + 3)/4 = (z - 6)/(-9)`


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.


S and S are the focii of the ellipse `x^2/a^2 + y^2/b^2 - 1` whose one of the ends of the minor axis is the point B If ∠SBS' = 90°, then the eccentricity of the ellipse is


The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs ₹ 48 per hour at 16 miles per hour. The most economical speed if the fixed charges i.e. salaries etc. amount to ₹ 300 per hour is


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


If the points (1, 1, λ) and (–3, 0, 1) are equidistant from the plane `barr*(3hati + 4hatj - 12hatk) + 13` = 0, find the value of λ.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×