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

Choose correct alternatives : The direction cosines of the normal to the plane 2x – y + 2z = 3 are ______ - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose correct alternatives :

The direction cosines of the normal to the plane 2x – y + 2z = 3 are ______ 

पर्याय

  • `(2)/(3),(-1)/(3),(2)/(3)`

  • `(-2)/(3),(1)/(3),(-2)/(3)`

  • `(2)/(3),(1)/(3),(2)/(3)`

  • `(2)/(3),(-1)/(3),(-2)/(3)`

MCQ

उत्तर

`(2)/(3),(-1)/(3),(2)/(3)`

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

संबंधित प्रश्‍न

Find the co-ordinates of the foot of the perpendicular drawn from the point `2hati - hatj + 5hatk` to the line `barr = (11hati - 2hatj - 8hatk) + λ(10hati - 4hatj - 11hatk).` Also find the length of the perpendicular.


A(1, 0, 4), B(0, -11, 13), C(2, -3, 1) are three points and D is the foot of the perpendicular from A to BC. Find the co-ordinates of D.


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.


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 :

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


Choose correct alternatives :

The equation of the plane in which the line `(x - 5)/(4) = (y - 7)/(4) = (z + 3)/(-5) and (x - 8)/(7) = (y - 4)/(1) = (z - 5)/(3)` lie, is


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


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


Find the direction ratios of the normal to the plane 2x + 3y + z = 7


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


If the normal to the plane has direction ratios 2, −1, 2 and it’s perpendicular distance from origin is 6, find its equation


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


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


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


If z1 and z2 are z-coordinates of the points of trisection of the segment joining the points A (2, 1, 4), B (–1, 3, 6) then z1 + z2 = ______.


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 ______


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 ______


XY-plane divides the line joining the points A(2, 3, -5) and B(1, -2, -3) in the ratio ______ 


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


A plane which passes through the point (3, 2, 0) and the line `(x - 3)/1 = (y - 6)/5, (z - 4)/4` 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 ______ 


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`.


If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to ______.


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 ______.


Reduce the equation `barr*(3hati - 4hatj + 12hatk)` = 3 to the normal form and hence find the length of perpendicular from the origin to the plane.


Find the vector equation of the line passing through the point (–2, 1, 4) and perpendicular to the plane `barr*(4hati - 5hatj + 7hatk)` = 15


A mobile tower is situated at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with three cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at point P(2, 3, 1) as shown in the figure below. The foot of the perpendicular from the point P on the plane is at the point `Q(43/29, 77/29, 9/29)`.


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.

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×