Vector Algebra

JEE Main 2025 (Online) 23rd January Evening ShiftMCQHard📈 Topic in 55% papers+4−1

Ques. 1JEE Main 2025, 23 January (Evening Shift)

Let the point A divide the line segment joining the points P(-1,-1,2) and Q(5,5,10) internally in the ratio r:1 (r>0). If O is the origin and ( OQ OA )- 15 | OP OA |2=10, then the value of r is :

Answer

(3) 7

Solution

A divides PQ in r:1: OA= OP+r OQr+1

[figure]

OQ OA= 10+150rr+1 and OP OA= rr+1( OP OQ), with OP OQ=(-20,20,0), | |2=800

10+150rr+1- 160r2(r+1)2=10 20r2-140r=0

r=7

Answer: (3)

Keep practising — Vector Algebra

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

Let c be the projection vector of b= i+4 k, >0, on the vector a= i+2 j+2 k. If | a+ c|=7, then the area of the parallelogram formed by the vectors b and c is .

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

Let a and b be two unit vectors such that the angle between them is 3. If a+2 b and 3 a- b are perpendicular to each other, then the number of values of in [-1,3] is :

All Vector Algebra PYQs →

PDFDownload Vector Algebra 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)