Show that the lines vecr= hati+hatj-hatk...

Show that the lines `vecr= hati+hatj-hatk+lambda(3hati-hatj)` and `vecr = 4 hati+hatk+mu(2hati+3hatk)` intersect. Also find the co[-ordinates of their point of intersection.

Text Solution

Verified by Experts

The correct Answer is:

`(4hati-hatk)`

Topper's Solved these Questions

THREE-DIMENSIONAL GEOMETRY
NAGEEN PRAKASHAN|Exercise Exercise 11 C|7 Videos
THREE-DIMENSIONAL GEOMETRY
NAGEEN PRAKASHAN|Exercise Exercise 11 D|35 Videos
THREE-DIMENSIONAL GEOMETRY
NAGEEN PRAKASHAN|Exercise Exercise 11 A|22 Videos
RELATIONS AND FUNCTIONS
NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos
VECTORS
NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Show that the lines bar (r) = ( hati + hatj - hatk) + lamda ( 3hati - hatj ) and bar(r) = ( 4hati - hatk ) + mu (2hati + 3hatk) intersect. Find their point of intersection .

Show that the lines : vec(r) = 3 hati + 2 hatj - 4 hatk + lambda (hati + 2 hatj + 2 hatk) and vec(r) = 5 hati - 2 hatj + mu (3 hati + 2 hatj + 6 hatk) (ii) vec(r) = (hati + hatj - hatk) + lambda (3 hati - hatj) . and vec(r) = (4 hati - hatk) + mu (2 hati + 3 hatk) are intersecting. Hence, find their point of intersection.

Show that the line vecr = (hati+hatj-hatk)+lambda(3hati-hatj) vecr = (4hati-hatk)+mu(2hati+3hatk) are coplanar. Also find the equation of plane in which these lines lie.

Find the shortest distance between the lines vecr = hati+ hatj+hatk+lambda(3hati-hatj) and vecr=4hati-hatk+mu(2hati+3hatk)

The equation of the plane containing the lines vecr=(hati+hatj-hatk)+lamda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk) , is

The lines vecr=(hati+hatj)+lamda(hati+hatk)andvecr=(hati+hatj)+mu(-hati+hatj-hatk) are

Show that the lines vecr=(2hatj-3hatk)+lambda(hati+2hatj+3hatk) and vecr = (2hati+6hatj+3hatk)+mu(2hati+3hatj+4hatk) are coplanar. Also the find the equation of the plane passing through these lines.

Find the shortest distance between the lines vecr = 3 hati + 2hatj - 4 hatk + lamda ( hati +2 hatj +2 hatk ) and vecr = 5 hati - 2hatj + mu ( 3hati + 2hatj + 6 hatk) If the lines intersect find their point of intersection

NAGEEN PRAKASHAN-THREE-DIMENSIONAL GEOMETRY -Exercise 11 B

The cartesian equation of a line is 6x+1=3y-2 = 3-2x. Find its directi...
Text Solution
|
Find the angle between the following pairs of lines (i) veci=3hati+2...
Text Solution
|
(i) Show that the line (x+3)/(2) = (y+1)/(-1) = (z+3)/(3) and (x)/(5) ...
Text Solution
|
Find the values of lambda if the following of lines perpendicular : ...
Text Solution
|
Show that the following pairs of lines intersect. Also find their poin...
Text Solution
|
Show that the lines (x-1)/(1) = (y-2)/(-1) = (z-1)/(1) and (x-1)/(1-...
Text Solution
|
Show that the lines vecr= hati+hatj-hatk+lambda(3hati-hatj) and vecr =...
Text Solution
|
Find the co-ordinates of that point at which the lines joining the poi...
Text Solution
|
Find the co-ordinates of that point at which the line joining the poin...
Text Solution
|
Find the co-ordinates of a point at which the line (x+1)/(2) = (y-3)/(...
Text Solution
|
Find the co-ordinates of a point at which the line (x+1)/(2) = (y-1)/(...
Text Solution
|
Find the co-ordiantes of the foot of perpendicular drawn from the poi...
Text Solution
|
Find the length and the foot of the perpendicular drawn from the point...
Text Solution
|
Find the co-ordinates of the foot of perpendicular and length of perp...
Text Solution
|
Find the image of the point (1,6,3) in the line x/1=(y-1)/2=(z-2)/3
Text Solution
|
Find the image of the point (0,2,3) in the line (x+3)/(5)= (y-1)/(2) =...
Text Solution
|
Find the image of the point (3hati-hatj+11hatk) in the line vecr = 2 h...
Text Solution
|
Find the shortest distance between the following lines : (i) vecr=4h...
Text Solution
|
Find the co-ordinates of the point at a distance of sqrt(5)units from ...
Text Solution
|
Find the co-ordinates of the point at a distance of sqrt(14) from the ...
Text Solution
|