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  1. Tardigrade
  2. Question
  3. Mathematics
  4. Three lines L1: vecr = λ hati, λ ∈ ℝ L2: vecr = hatk + μ hatj, μ ∈ ℝ and L3: vecr = hati + hatj + v hatk, v ∈ ℝ are given. For which point(s) Q on L2 can we find a point P on L1 and a point R on L3 so that P, Q and R are collinear?

Q. Three lines

and

are given. For which point(s) on can we find a point P on and a point R on so that P, Q and R are collinear?

JEE Advanced JEE Advanced 2019 Report Error

Solution:

Let be points. and respectively
Since are collinear, iscollinear with
Hence
For every there exist unique
Hence Q cannot have coordinates and

Questions from JEE Advanced 2019

1. Let be given by

Then which of the following options is/are correct?

2. Let f : ℝ ℝ be given by f(x) = (x - 1)(x - 2)(x - 5). Define

Then which of the following options is/are correct?

3. Three lines

and

are given. For which point(s) on can we find a point P on and a point R on so that P, Q and R are collinear?

4. Let f(x) = sin( cos x) and g(x) = cos(2 sin a) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order:
X = {x : f'(x) — 0}, Y = {x : f(x) = 0},
Z = [x : g(x) = 0}, W = [x : g'(x) = 0}.
List -1 contains the sets X, Y, Z and W. List - II contains some information regarding these sets.
List-I List-II
(I) X (p) ⊇
(II) Y (Q) an arithmetic progression
(III) Z (R) NOT an arithmetic progression
(IV) W (S) ⊇
(T) ⊇
(U) ⊇


Question: Which of the following is the only CORRECT combination?

5. Let f(x) = sin( cos x) and g(x) = cos(2 sin a) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order:
X = {x : f'(x) — 0}, Y = {x : f(x) = 0},
Z = [x : g(x) = 0}, W = [x : g'(x) = 0}.
List -1 contains the sets X, Y, Z and W. List - II contains some information regarding these sets.
List-I List-II
(I) X (p) ⊇
(II) Y (Q) an arithmetic progression
(III) Z (R) NOT an arithmetic progression
(IV) W (S) ⊇
(T) ⊇
(U) ⊇


Question : Wliich of the following is the only CORRECT combination?

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