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Three Dimensional Geometry

JEE Main 2025 (Online) 22nd January Morning ShiftMCQHard📈 Topic in 34% papers+4−1
Ques. 1JEE Main 2025, 22 January (Morning Shift)

Let L1: x-12= y-23= z-34 and L2: x-23= y-44= z-55 be two lines. Then which of the following points lies on the line of the shortest distance between L1 and L2 ?

  1. ( 143,-3, 223 )
  2. (2,3, 13 )
  3. ( 83,-1, 13 )
  4. (- 53,-7,1 )

Answer

(1) ( 143,-3, 223 )

Solution

The shortest distance line is the common perpendicular: direction b1 b2=(-1,2,-1).

P=(2 +1, 3 +2, 4 +3), Q=(3 +2, 4 +4, 5 +5) with PQ (-1,2,-1)

= 13, =- 16, so P= ( 53,3, 133 )

Required line: through P with direction (1,-2,1)

Option (1): ( 143,-3, 223 )-P=(3,-6,3) (1,-2,1), so it lies on the line.

Answer: (1)

Keep practising — Three Dimensional Geometry

Ques. 2JEE Main 2025, 22 January (Morning Shift)

Let L1: x-13= y-1-1= z+10 and L2: x-22= y0= z+4 , , be two lines, which intersect at the point B. If P is the foot of perpendicular from the point A(1,1,-1) on L2, then the value of 26 (PB)2 is .

Ques. 3JEE Main 2025, 22 January (Evening Shift)

Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vector 3 i+2 j+2 k. If the distance of the point Q from the point R(1,3,3) is 5, then the square of the area of PQR is equal to :

  1. 148
  2. 144
  3. 136
  4. 140
Ques. 4JEE Main 2025, 22 January (Evening Shift)

The perpendicular distance, of the line x-12= y+2-1= z+32 from the point P(2,-10,1), is :

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

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