Home
Class 12
MATHS
Find the equation of a plane containing ...

Find the equation of a plane containing the line of intersection of the planes `x+y+z-6=0a n d2x+3y+4z+5=0` passing through `(1,1,1)` .

Text Solution

AI Generated Solution

To find the equation of a plane containing the line of intersection of the planes \(x + y + z - 6 = 0\) and \(2x + 3y + 4z + 5 = 0\) that passes through the point \((1, 1, 1)\), we can follow these steps: ### Step 1: Write the equation of the plane The equation of a plane that contains the line of intersection of two planes can be expressed as a linear combination of the equations of the two planes. Thus, we can write the equation of the required plane as: \[ x + y + z - 6 + \lambda(2x + 3y + 4z + 5) = 0 \] ...
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 3.1|12 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 3.2|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives (Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

The equation of a plane containing the line of intersection of the planes 2x-y-4=0 and y+2z-4=0 and passing through the point (1, 1, 0) is

Find the vector equation (in scalar product form) of the plane containing the line of intersection of the planes x-3y+2z-5=0\ a n d\ 2x-y+3z-1=0\ a n d passing through (1,\ -2,\ 3)dot

Find the equation of the plane through the line of intersection of the planes x+2y+3z+4=0\ a n d\ x-y+z+3=0 and passing through the origin.

Find the equation of the plane which contains the line of intersection of the planes x+2y+3z-4=0a n d2x+y-z+5=0 and which is perpendicular to the plane 5x+3y-6z+8=0.

Find the equation of the plane passing through the line of intersection of the planes 4x-5y-4z=1 and 2x+y+2z=8 and the point (2,1,3).

Find the equation of plane passing through the line of intersection of planes 3x+4y-4=0 and x+7y+3z=0 and also through origin.

STATEMENT-1 : The equation of the plane through the intersection of the planes x+ y+z= 6 and 29x + 23y+ 17 z = 276 and passing through (1,1,1), is 5x + 4y + 3z = 47 and STATEMENT-2 : Equation of the plane through the line of intersection of the planes P_(1)= 0 and P_(2) = 0 is P_(1)+lambdaP_(2) =0, lambda ne 0,

The equation of a plane passing through the line of intersection of the planes : x+2y+z-10=0 and 3x+y-z=5 and passing through the origin is :

Find the equation of a plane passing through the intersection of the planes x-3y+2z-5 - 0 and 2x-y+3z-1 = 0 and passes through the point (1,-2,3) .

Find the equation of the plane passing through the intersection of the planes: x+y+z+1=0 and 2x-3y +5z-2=0 and the point (-1, 2,1)