मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Choose correct alternatives : 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

Advertisements
Advertisements

प्रश्न

Choose correct alternatives :

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

पर्याय

  • 4x + y + 5z = 14

  • 4x – 2y – 5z = 45

  • x – 2y – 5z = 10

  • 4x + y + 6z = 11

MCQ
Advertisements

उत्तर

4x – 2y – 5z = 45.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Line and Plane - Miscellaneous Exercise 6 B [पृष्ठ २२५]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 6 Line and Plane
Miscellaneous Exercise 6 B | Q 20 | पृष्ठ २२५

संबंधित प्रश्‍न

Find the length of the perpendicular (2, –3, 1) to the line `(x + 1)/(2) = (y - 3)/(3) = (z + 1)/(-1)`.


Find the perpendicular distance of the point (1, 0, 0) from the line `(x - 1)/(2) = (y + 1)/(-3) = (z + 10)/(8)` Also find the co-ordinates of the foot of the perpendicular.


If the lines `(x - 1)/2 = (y + 1)/3 = (z - 1)/4 and (x - 3)/1 = (y - k)/2 = z/1` intersect each other, then find k.


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


Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x + 6y – 3z = 63.


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`.


Show that the line `bar"r" = (2hat"j" - 3hat"k") + lambda(hat"i" + 2hat"j" + 3hat"k") and bar"r" = (2hat"i" + 6hat"j" + 3hat"k") + mu(2hat"i" + 3hat"j" + 4hat"k")` are coplanar. Find the equation of the plane determined by them.


Find the co-ordinates of the foot of the perpendicular drawn from the point (0, 2, 3) to the line `(x + 3)/(5) = (y - 1)/(2) = (z + 4)/(3)`.


Choose correct alternatives:

If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is ______.


Choose correct alternatives :

The lines `x/(1) = y/(2) = z/(3) and (x - 1)/(-2) = (y - 2)/(-4) = (z - 3)/(6)` are


Choose correct alternatives :

Equation of X-axis is ______.


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


Choose correct alternatives :

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


Choose correct alternatives :

The equation of the plane passing through the points (1, −1, 1), (3, 2, 4) and parallel to the Y-axis is ______  


If the planes 2x – my + z = 3 and 4x – y + 2z = 5 are parallel then m = ______ 


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


Find the vector equation of a plane at a distance 6 units from the origin and to which vector `2hat"i" - hat"j" + 2hat"k"` is normal


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


Show that the lines `(x + 1)/(-10) = (y + 3)/(-1) = (z - 4)/(1)` and `(x + 10)/(-1) = (y + 1)/(-3) = (z - 1)/4` intersect each other.also find the coordinates of the point of intersection


The equation of a plane containing the point (1, - 1, 2) and perpendicular to the planes 2x + 3y - 2z = 5 and x + 2y - 3z = 8 is ______.


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 ______


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


The equation of the plane through (1, 2, -3) and (2, -2, 1) and parallel to the X-axis is ______ 


Equation of the plane perpendicular to the line `x/1 = y/2 = z/3` and passing through the point (2, 3, 4) is ______


The equation of the plane through the point (2, -1, -3) and parallel to the lines `(x - 1)/3 = (y + 2)/2 = z/(-4)` and `x/2 = (y - 1)/(-3) = (z - 2)/2` is ______


The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is ______ 


The distance of the point (1, 0, 2) from the point of intersection of the line `(x - 2)/3 = (y + 1)/4 = (z - 2)/12` and the plane x - y + z = 16, is ______ 


Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 3y + 5 = 0.


Let the line `(x - 2)/3 = (y - 1)/(-5) = (z + 2)/2` lie in the plane x + 3y - αz + β = 0. Then, (α, β) equals ______ 


If the plane x - 3y + 5z = d passes through the point (1, 2, 4), then the lengths of intercepts cut by it on the axes of X, Y, Z are respectively ______ 


If the line `(x + 1)/2 = (y - 5)/3 = (z - "p")/6` lies in the plane 3x – 14y + 6z + 49 = 0, then the value of p is ______.


Find the vector equation of the plane passing through the point A(–1, 2, –5) and parallel to the vectors `4hati - hatj + 3hatk` and `hati + hatj - hatk`.


Let P be a plane passing through the points (1, 0, 1), (1, –2, 1) and (0, 1, –2). Let a vector `vec"a" = αhat"i" + βhat"j" + γhat"k"` be such that `veca` is parallel to the plane P, perpendicular to `(hat"i"+2hat"j"+3hat"k")`and `vec"a".(hat"i" + hat"j" + 2hat"j")` = 2, then (α – β + γ)2 equals ______.


If A and B are foot of perpendicular drawn from point Q(a, b, c) to the planes yz and zx, then equation of plane through the points A, B and O is ______.


The equation of the plane passes through the point (2, 5, –3) perpendicular to the plane x + 2y + 2z = 1 and x – 2y + 3z = 4 is ______.


Find the equation of plane which is at a distance of 4 units from the origin and which is normal to the vector `2hati - 2hatj + hatk`.


Find the point of intersection of the line `(x + 1)/2 = (y - 1)/3 = (z - 2)/1` with the plane x + 2y – z = 6.


Find the equation of the plane containing the line `x/(-2) = (y - 1)/3 = (1 - z)/1` and the point (–1, 0, 2).


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×