The perpendicular distance between the l...

The perpendicular distance between the line `vecr = 2hati-2hatj+3hatk+lambda(hati-hatj+4hatk)` and the plane `vecr.(hati + 5hatj + hatk) = 5` is :

`10/(3sqrt(3))`

`10/3`

`10//9`

none of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

PLANE AND STRAIGHT LINE IN SPACE
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|31 Videos
PLANE AND STRAIGHT LINE IN SPACE
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|16 Videos
MISCELLANEOUS EQUATIONS AND INEQUATIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos
PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

Similar Questions

Explore conceptually related problems

Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) and the plane vecr.(3hati+2hatj-hatk)=4 is

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

Find the angle between the line vecr = (2hati+hatj-hatk)+lambda(2hati+2hatj+hatk) and the plane vecr.(6hati-3hatj+2hatk)+1=0 .

The angle between the line vecr = ( 5 hati - hatj - 4 hatk ) + lamda ( 2 hati - hatj + hatk) and the plane vec r.( 3 hati - 4 hatj - hatk) + 5=0 is

The line vecr = 2hati - 3 hatj - hatk + lamda ( hati - hatj + 2 hatk ) lies in the plane vecr. (3 hati + hatj - hatk) + 2=0 or not

Find the points of intersection of the line vecr = (2hati - hatj + 2hatk) + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

Find the distance of the point (-1,-5,-10) from the point of the intersection of the line vecr = 2hati-2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk) = 5 .

If the point of intersection of the line vecr = (hati + 2 hatj + 3 hatk ) + lambda( 2 hati + hatj+ 2hatk ) and the plane vecr (2 hati - 6 hatj + 3 hatk) + 5=0 lies on the plane vec r ( hati + 75 hatj + 60 hatk) -alpha =0, then 19 alpha + 17 is equal to :

Find the shortest distance between the lines vecr = 2hati - hatj + hatk + lambda(3hati - 2hatj + 5hatk), vecr = 3hati + 2hatj - 4hatk + mu(4hati - hatj + 3hatk)

Shortest distance between the lines: vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+u(2hati+4hatj-5hatk)

OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Exercise

Find the vector equation of the plane in which the lines vecr=hati+ha...
Text Solution
|
The Cartesian equation of the plane vecr=(1+lamda-mu)hati+(2-lamda)hat...
Text Solution
|
The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...
Text Solution
|
The vector equation of the line of intersection of the planes vecr.(2h...
Text Solution
|
A straight line vecr=veca+lambda vecb meets the plane vecr. vec n=0 at...
Text Solution
|
The equation of the plane passing through three non - collinear points...
Text Solution
|
The length of the perpendicular from the origin to the plane passing t...
Text Solution
|
The equation of the plane containing the line (x-x1)/l=(y-y1)/m=(z-...
Text Solution
|
Find the shortest distance between the following pairs of lines whose ...
Text Solution
|
If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...
Text Solution
|
The direction ratios of a normal to the plane passing throuhg (0,0,1)...
Text Solution
|
A variable plane is at a distance, k from the origin and meets the coo...
Text Solution
|
Find the equation of the plane perpendicular to the line (x-1)/2=(y...
Text Solution
|
Find the equation of the plane through the points (2,2,1) and (9,3,6) ...
Text Solution
|
The equation of the plane containing the two lines (x-1)/2=(y+1)/(-1...
Text Solution
|
The direction ratios of the normal to the plane passing through the po...
Text Solution
|
The equation of a plane through the point (2, 3, 1) and (4, -5, 3) a...
Text Solution
|
The angle between the lines (x+4)/(1) = (y-3)/(2) = (z+2)/(3) and (x)/...
Text Solution
|
The equation of the plane which is perpendicular bisector of the line ...
Text Solution
|
If the position vectors of the point A and B are 3hat(i)+hat(j)+2hat(k...
Text Solution
|