हिंदी

The perpendicular distance of the plane 2x + 3y – z = k from the origin is 14 units, the value of k is ______.

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प्रश्न

The perpendicular distance of the plane 2x + 3y – z = k from the origin is `sqrt(14)` units, the value of k is ______.

विकल्प

  • 14

  • 196

  • `2sqrt(14)`

  • `sqrt(14)/(2)`

MCQ
रिक्त स्थान भरें
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उत्तर

The perpendicular distance of the plane 2x + 3y – z = k from the origin is `sqrt(14)` units, the value of k is 14.

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अध्याय 6: Line and Plane - Miscellaneous Exercise 6 B [पृष्ठ २२४]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 6 Line and Plane
Miscellaneous Exercise 6 B | Q 11 | पृष्ठ २२४

संबंधित प्रश्न

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Find the vector equation of a plane which is at 42 unit distance from the origin and which is normal to the vector `2hati + hatj - 2hatk`.


Reduce the equation `bar"r".(3hat"i" + 4hat"j" + 12hat"k")` to normal form and hence find
(i) the length of the perpendicular from the origin to the plane
(ii) direction cosines of the normal.


Find the vector equation of the plane passing through the point having position vector `hati + hatj + hatk` and perpendicular to the vector `4hati + 5hatj + 6hatk`.


Choose correct alternatives :

The equation of the plane passing through (2, -1, 3) and making equal intercepts on the coordinate axes is


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The foot of perpendicular drawn from the point (0,0,0) to the plane is (4, -2, -5) then the equation of the plane is


Solve the following :

Find the perpendicular distance of the origin from the plane 6x + 2y + 3z - 7 = 0


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If the foot of the perpendicular drawn from the origin to the plane is (4, −2, -5), then the equation of the plane is ______ 


The coordinates of the foot of perpendicular drawn from the origin to the plane 2x + y − 2z = 18 are ______ 


Find direction cosines of the normal to the plane `bar"r"*(3hat"i" + 4hat"k")` = 5


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Find the equation of the plane passing through the point (7, 8, 6) and parallel to the plane `bar"r"*(6hat"i" + 8hat"j" + 7hat"k")` = 0


If the line `(x - 3)/2 = (y + 2)/-1 = (z + 4)/3` lies in the plane lx + my - z = 9, then l2 + m2 is equal to ______


If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is ______


The intercepts of the plane 3x - 4y + 6z = 48 on the co-ordinate axes are ______


Equations of planes parallel to the plane x - 2y + 2z + 4 = 0 which are at a distance of one unit from the point (1, 2, 3) are _______.


Equation of plane parallel to ZX-plane and passing through the point (0, 5, 0) is ______


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Answer the following questions.

  1. Find the equation of the plane containing the points A, B and C.
  2. Find the equation of the line PQ.
  3. Calculate the height of the tower.

The Cartesian equation of a plane through A (7, 8, 6) and parallel to the XY plane is


If the plane \[\frac{x}{3}+\frac{y}{2}-\frac{z}{4}=1\] cuts the coordinate axes at points A, B and C, then the area of the X triangle ABC is


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