Show that the line L whose vector equati...

Show that the line L whose vector equation is `vecr=2hati-2hatj+3hatk+lambda(hati-hatj+4hatk) ` is parallel to the plane `pi` whose vector equation is `vecr*(hati+5hatj+hatk)=5` and find the distance between them.

Topper's Solved these Questions

THREE DIMENSIONAL GEOMETRY
PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos
RELATIONS AND FUNCTIONS
PRADEEP PUBLICATION|Exercise EXERCISE|401 Videos
VECTORS
PRADEEP PUBLICATION|Exercise EXERCISE|438 Videos

Similar Questions

Explore conceptually related problems

Show that the plane whose vector equation is vecr.(hati+2hatj-hatk)=3 contains the line whose vector equation is vecr=hati+hatj+lambda(2hati+hatj+4hatk) .

State when the line vecr=veca+lambdavecb is parallel to the plane vecr*vecn=d . Show that the line vecr=hati+hatj+lambda (2hati+hatk+4hatk) is parallel to the plane vecr*(-2hati+hatk)=5 . Also, find the distance between the line and the plane.

Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

Find the shortest distance between the lines whose vector equations are vecr = (hati+2hatj+3hatk) +lambda(hati-3hatj+2hatk) and vecr = 4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

Find the shortest distance between the following lines whose vector equations are : vecr=6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk) and vecr=-4hati-hatk+mu(3hati-2hatj-2hatk)

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =4.

Show that the lines vecr=hati+hatj+hatk+lambda(hati-hatj+hatk) and vecr=4hatj+2hatk+mu(2hati-hatj+3hatk) are coplanar.

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE

Find the equations of two planes through the point (4,2,1),(2,1,-1) an...
Text Solution
|
Find the length of the projection of the line segment joining the poin...
Text Solution
|
Show that the line L whose vector equation is vecr=2hati-2hatj+3hatk+l...
Text Solution
|
Find the equation of plane passing through the point (1,4,-2) and para...
Text Solution
|
Find the equation of the planes parallel to the plane x-2y+2z-3=0 and ...
Text Solution
|
The planes 2x-2y+4z+5=0 and 3x-3y+6z-1=0 are
Text Solution
|
Find the distance between the parallel planes 2x-y+3z+4=0 and 6x-3y+9z...
Text Solution
|
Show that the equation of the plane through the line x/l=y/m=z/n and p...
Text Solution
|
Two systems of rectangular axes have the same origin. If a plane cuts ...
Text Solution
|
Show that the points P(hati-hatj+3hatk) and Q(3hati+3hatj+3hatk) are e...
Text Solution
|
Find in parametric form, the equations of the line x+y+z+1=0, 4x+y-2z+...
Text Solution
|
Find the equation of the plane through the line of intersection of the...
Text Solution
|
Find the equation of the plane containing the line of intersection of ...
Text Solution
|
Find the vector quation of the plane containing the line of intersecti...
Text Solution
|
Find the equation of the plane which is perpendicular to the plane 5 x...
Text Solution
|
Find the equation of the plane bisectiing the angles between the plane...
Text Solution
|
Show that the lines (x+4)/3=(y+6)/5=(z-1)/-2 and 3x-2y+z+5=0=2x+3y+4z-...
Text Solution
|
Prove that the line of section of the planes 5x+2y-4z+2=0 and 2x+8y+2z...
Text Solution
|
Find the equations of the line through the point (1,2,4) and parallel ...
Text Solution
|
Find the angle between the lines: x-2y+z=0=x+2y-2z and x+2y+z=0=3x+9y+...
Text Solution
|