Home
Class 12
MATHS
Find the cartesian and vector equations ...

Find the cartesian and vector equations of the planes through the line of intersection of the planes `vec r.(2hati+6hatj)+12=0` and `vec r.(3hati-hatj+4hatk)=0` which are at a unit distance from the origin.

Text Solution

Verified by Experts

The correct Answer is:
`2x+y+2z+3=0,-x+2y-2z+3=0` and `vec r.(2hati+hatj+2hatk)+3=0, vec r.(-hati+2hatj-2hatk)+3=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the equation of the plane passing through the line of intersection of the plane vecr.(hati+3 hatj)+6=0 and vecr.(3 hati- hatj-4k)=0 which is at a unit distance from the origin.

Find the equation of the plane passing through the line of intersection of the planes vec r.(hati+hatj+hatk)=1 and vec r.(2hati+3hatj-hatk)+4=0 and parallel to x-axis.

Find the vector equation of the line passing through the point (2,-3,1) and parallel to the planes vec r.(2hati-3hatj-hatk)=3 and vec r.(hati+hatj-hatk)=4 .

Find the equation of the plane though the line of intersection of the planes vecr.(2 hati-3 hatj+ 4 hatk)=1 and vecr.( hati- hatj)+4=0 and prependicular to vecr.(2 hati- hatj+ hatk)+8=0 .

The angle between hati and line of the intersection of the planes vecr.( hati+2 hatj+ 3 hatk)=0 and vecr.(3 hati+3 hatj+ hatk)=0 is __

The vector equation of the plane passing through the origin and the line of intersection of the planes vec r. vec a = lambda and vec r. vec b =mu is __

A unit vector parallel to the intersection of planes vecr.( hati- hatj + hat k)=5 and vec r .(2 hati+ hatj-3 hatk)=4 is ___

Find the equation of the plane which constant the line of intesection of the planes vecr.( hati+2 hatj+3 hatk)-4=0 and vecr.( 2 hati+ hatj-hatk)=0 and which is prependicular to the plane vecr.(5 hati+3 hatj-6 hatk)+8=0.

Find the angle between the plane vecr.(2 hati-hatj+2 hat k)=6 and vecr.(3 hati+6 hatj-2 hatk) =9

Find the vector equations of the plane passing through the points 3 hati+ 4 hatj+2 hatk, 2hati-2 hatj -hatk and 7 hati+6 hatk .