Home
Class 12
MATHS
Find the equation of the plane passing t...

Find the equation of the plane passing through the line intersection of the plane: `vec2x-y=0 and 3z-y=0` and perpendicular to the plane `4x+5y-3z=8`

Text Solution

Verified by Experts

The equation of the plane through the line of intersection of the planes `2x - y = 0 and 3z - y = 0 `
may be written as `(2x-y) +k(3z - y) = 0`
`rArr 2x -(1+k)y+3kz =0`
which will be perpendicular to the plane
`4x + 5y- 3z 8`
if `8 - 5(1+k) - 9k = 0`
`rArr 8 - 5 -5k - 9k =0`
`rArr k= 3/14`
Raquired equation of the plane is
`2x-(1+3/14)y+3 (3)/14 z=0`
`rArr 28 x - 17 y +9z = 0.`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise Illustration|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise TRY YOURSELF|97 Videos

  • STRAIGHT LINES

    AAKASH INSTITUTE|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Section - J (Akash Challengers Question)|15 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the plane passing through the line intersection of the plane: 2x-y=0 and 3z-y=0 and perpendicular to the plane 4x+5y-3z=8

Find the equation of the plane passing through the line of intersection of the planes 2x-y=0 and 3z-y=0 , and perpendicular to the plane 4x+5y-3z=9 .

Let P=0 be the equation of a plane passing through the line of intersection of the planes 2x-y=0 and 3z-y=0 and perpendicular to the plane 4x+5y-3z=8. Then the points which lie on the plane P=0 is/are a.(0,9,17) b.(1/7,21/9) c.(1,3,-4) d.(1/2,1,1/3)

Find the equation of the plane passing through the intersection of the planes 2x-3y+z-4=0 and x-y+z+1=0 and perpendicular to the plane x+2y-3z+6=0

The equation of the plane passing through the line of intersection of the planes x+y+z=6 and 2x+3y+4z+5=0 and perpendicular to the plane 4x+5y-3z=8 is

Find the equation of the plane passing through the intersection of the planes 2x+3y-z+1=0 and x+y-2z+3=0 and perpendicular to the plane 3x-y-2z-4=0

Find the equation of the plane through the line of intersection of the planes x+2y+3z+2=0 , 2x+3y-z+3=0 and perpendicular to the plane x+y+z=0

The equation of the plane passing through the line of intersection of the planes x+y+z=1,2x+3y+4z=7 , and perpendicular to the plane x-5y+3z=5 is given by

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0