Three Dimensional Geometry

JEE Main 2025 (Online) 22nd January Morning ShiftNumericalMedium📈 Topic in 74% papers+4

Ques. 1JEE 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 .

Answer

216

Solution

Equating points of L1 and L2: B=(4,0,-1) and =3. A(1,1,-1) lies on L1 (at t=0), so PB is the projection of AB on L2.

[figure]

AB=(3,-1,0), d=(2,0,3): PB= | AB d|| d|= 6 13

26 (PB)2=26 3 3613=216

Answer: 216

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Ques. 2JEE 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 :

Ques. 3JEE 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 :

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