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Three Dimensional Geometry

JEE Main 2024 (Online) 9th April Morning ShiftMCQMedium📈 Topic in 36% papers+4−1
Ques. 1JEE Main 2024, 9 April (Morning Shift)

Let the line L intersect the lines x - 2 = -y = z - 1, 2(x + 1) = 2(y - 1) = z + 1 and be parallel to the line x - 23 = y - 11 = z - 22. Then which of the following points lies on L ?

  1. (- 13, 1, -1 )
  2. (- 13, -1, 1 )
  3. (- 13, -1, -1 )
  4. (- 13, 1, 1 )

Answer

(1) (- 13, 1, -1 )

Solution

Point on the first line: M( + 2, - , + 1)

Second line is x + 1 = y - 1 = z + 12, so a point on it is N( - 1, + 1, 2 - 1).

L = MN is parallel to (3, 1, 2), so the d.r.'s of MN, ( - + 3, - - - 1, - 2 + 2), are proportional to 3 : 1 : 2:

- + 3 = 3(- - - 1) 2 + = -3

- 2 + 2 = 2(- - - 1) = - 43, hence = - 13

So M ( 23, 43, - 13 ) and L: x - 233 = y - 431 = z + 132 = t

For x = - 13: t = - 13, which gives y = 1, z = -1, i.e. the point (- 13, 1, -1 ).

Answer: (1)

Keep practising — Three Dimensional Geometry

Ques. 2JEE Main 2024, 9 April (Evening Shift)

Consider the line L passing through the points (1, 2, 3) and (2, 3, 5). The distance of the point ( 113, 113, 193 ) from the line L along the line 3x - 112 = 3y - 111 = 3z - 192 is equal to

  1. 6
  2. 3
  3. 5
  4. 4
Ques. 3JEE Main 2024, 9 April (Evening Shift)

The square of the distance of the image of the point (6, 1, 5) in the line x - 13 = y2 = z - 24, from the origin is .

Ques. 4JEE Main 2024, 8 April (Morning Shift)

If the shortest distance between the lines L1 : r = (2 + ) i + (1 - 3 ) j + (3 + 4 ) k, R L2 : r = 2(1 + ) i + 3(1 + ) j + (5 + ) k, R is m n, where (m, n) = 1, then the value of m + n equals

  1. 384
  2. 387
  3. 390
  4. 377
Ques. 5JEE Main 2024, 8 April (Evening Shift)

If the shortest distance between the lines x - 2 = y - 43 = z - 34 and x - 24 = y - 46 = z - 78 is 13 29, then a value of is :

  1. 1325
  2. 1
  3. -1
  4. - 1325
Ques. 6JEE Main 2024, 8 April (Evening Shift)

Let P( , , ) be the image of the point Q(1, 6, 4) in the line x1 = y - 12 = z - 23. Then 2 + + is equal to

Ques. 7JEE Main 2024, 6 April (Morning Shift)

The shortest distance between the lines x - 32 = y + 15-7 = z - 95 and x + 12 = y - 11 = z - 9-3 is

  1. 8 3
  2. 6 3
  3. 5 3
  4. 4 3
Ques. 8JEE Main 2024, 6 April (Morning Shift)

Let P be the point (10, -2, -1) and Q be the foot of the perpendicular drawn from the point R(1, 7, 6) on the line passing through the points (2, -5, 11) and (-6, 7, -5). Then the length of the line segment PQ is equal to .

Ques. 9JEE Main 2024, 6 April (Evening Shift)

Let P( , , ) be the image of the point Q(3, -3, 1) in the line x - 01 = y - 31 = z - 1-1 and R be the point (2, 5, -1). If the area of the triangle PQR is and 2 = 14K, then K is equal to :

  1. 18
  2. 81
  3. 72
  4. 36
Ques. 10JEE Main 2024, 6 April (Evening Shift)

If the shortest distance between the lines x - 3 = y - 2-1 = z - 11 and x + 2-3 = y + 52 = z - 44 is 44 30, then the largest possible value of | | is equal to .

Ques. 11JEE Main 2024, 5 April (Morning Shift)

If the line 2 - x3 = 3y - 24 + 1 = 4 - z makes a right angle with the line x + 33 = 1 - 2y6 = 5 - z7, then 4 + 9 is equal to :

  1. 4
  2. 13
  3. 5
  4. 6

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