Home
Class 12
MATHS
The position vector of the point where t...

The position vector of the point where the line `vec(r)=hat(i)-hat(j)+hat(k)+t(hat(i)+hat(j)-hat(k))` meets the plane `vec(r)*(hat(i)+hat(j)+hat(k))=5`, is
(A) `5hati+hatj-hatk`
(B) `5hati+3hatj-3hatk`
(C) `5hati+hatj+hatk`
(D) `4hati+2hatj-2hatk`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Find the image of the point having position vector hat(i) + 3hat(j) + 4hat(k) in the plane vec(r ).(2hat(i) - hat(j) + hat(k))+ 3=0

Find the angle between the line vec r = (2 hat i-hat j +3 hat k)+ lambda (3 hat i-hat j+2 hat k ) and the plane vec r.(hat i + hat j + hat k)=3

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

If vec(A)=2hat(i)+hat(j)+hat(k) and vec(B)=hat(i)+hat(j)+hat(k) are two vectors, then the unit vector is

Find the shortest distance between the lines vec r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and vec r=(2 hat i- hat j- hat k)+mu(2 hat i+ hat j+2 hat k)

A vector parallel to the line of intersection of the planes overset(to)( r) (3 hat(i) - hat(j) + hat(k) )=5 and overset(to) (r ) (hat(i) +4 hat(j) - 2 hat(k) )=3 is

Unit vectors perpendicular to the plane of vectors vec(a) = 2 hat(*i) - 6 hat(j) - 3 hat(k) and vec(b) = 4 hat(i) + 3 hat(j) - hat(k) are

Prove that lines vec( r)= (hat(i)+ hat(j) + hat(k))+ t(hat(i) - hat(j) + hat(k)) and vec(r ) = (3hat(i) - hat(k)) + s(4hat(j) - 16hat(k)) intersect. Also find the position vector of their point of intersection

Find the shortest distance between the lines vec r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and vec r=2 hat i- hat j- hat k+mu(2 hat i+ hat j+2 hat k)

If vec(a) = hat(i) - 2 hat(j) + 3 hat(k) and vec(b) = 2 hat(i) - 3 hat(j) + 5 hat(k) , then angle between vec(a) and vec(b) is