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 ?

( 143,-3, 223 )
(2,3, 13 )
( 83,-1, 13 )
(- 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 :

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 :

All Three Dimensional Geometry PYQs →

PDFDownload Three Dimensional Geometry PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Main Mathematics chapters

Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)