Home
Class 12
MATHS
The planes: 2x y + 4z = 5 a n d 5x 2. ...

The planes: `2x y + 4z = 5 a n d 5x 2. 5 y + 10 z = 6`are(A) Perpendicular (B) Parallel(C) intersect y-axis (D) passes through `(0,0,5/4)`

Text Solution

AI Generated Solution

To determine the relationship between the two planes given by the equations \(2x - y + 4z = 5\) and \(5x - 2.5y + 10z = 6\), we will analyze their normal vectors and check for conditions of parallelism or perpendicularity. ### Step 1: Identify the normal vectors of the planes The general form of a plane is given by the equation \(Ax + By + Cz = D\), where \((A, B, C)\) is the normal vector of the plane. For the first plane \(P_1: 2x - y + 4z = 5\): - The normal vector \(N_1\) is \((2, -1, 4)\). ...
Promotional Banner

Similar Questions

Explore conceptually related problems

The planes : 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are

The planes 2x - y + 4z = 3 and 5x - 2.5y + 10z = 6 are :

The plane through the intersection of the planes x + y - z = 1 and 2x + 3y + Z + 4 = 0 and parallel to z-axis also passes through the point (A) (-3,0, -1) (B) (3,3, - 1) (C) (3, 2, 1) (D) (3, -3,0)

If the planes 2x-y+lamdaz-5=0 an x+4y+2z-7=0 are perpendicular then lamda=

The plane x + 3y + 13 = 0 passes through the line of intersection of the planes 2x - 8y + 4z = p and 3x - 5y + 4z + 10 =0 . If the plane is perpendicular to the plane 3x - y - 2z - 4 = 0 , then the value of p is equal to

The plane x + 3y + 13 = 0 passes through the line of intersection of the planes 2x - 8y + 4z = p and 3x - 5y + 4z + 10 = 0 If the plane is perpendicular to the plane , 3x - y - 2z - 4 = 0 then the value of p is equal to

The planes 3x - y + z + 1 = 0 , 5x + y + 3z = 0 intersect in the line PQ. The equation of the plane through the point (2,1,4) and the perpendicular to PQ is

The plane x+y=0 (A) is parallel to y-axis (B) is perpendicular to z-axis (C) passes through y-axis (D) none of these

The lines (x-1)/(2)=(y-2)/(4)=(z-3)/(7) and (x-1)/(4)=(y-2)/(5)=(z-3)/(7) are (A) perpendicular (B) intersecting (C) skew (D) parallel

(i) Find the equation of the plane passing through (1,-1,2) and perpendicular to the planes : 2 x + 3y - 2z = 5 , x + 2y - 3z = 8 . (ii) find the equation of the plane passing through the point (1,1,-1) and perpendicular to each of the planes : x + 2y + 3z - 7 = 0 and 2x - 3y + 4z = 0 . (iii) Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to the planes : 3x + 2y - 3z = 1 and 5x - 4y + z = 5.