Vector Algebra · Question 3

JEE Advanced 2025 Paper 1NumericalMedium📈 Topic in 17% papers+4

For any two points M and N in the XY-plane, let MN denote the vector from M to N, and 0 denote the zero vector. Let P, Q and R be three distinct points in the XY-plane. Let S be a point inside the triangle PQR such that SP + 5 SQ + 6 SR = 0. Let E and F be the mid-points of the sides PR and QR, respectively. Then the value of length of the line segment EFlength of the line segment ES is .

Answer

1.15 to 1.25

Solution

With position vectors p, q, r, s: ( p - s) + 5( q - s) + 6( r - s) = 0 s = p + 5 q + 6 r12.

e = p + r2, f = q + r2, so EF = q - p2 and EF = PQ2.

ES = p + 5 q + 6 r12 - 6 p + 6 r12 = 5( q - p)12, so ES = 5PQ12.

EFES = 1/25/12 = 65 = 1.2.

Answer: 1.2

JEE Advanced 2025 Paper 1

Keep practising — Vector Algebra

Let w = i + j - 2 k, and u and v be two vectors, such that u v = w and v w = u. Let , , , and t be real numbers such that u = i + j + k, -t + + = 0, - t + = 0, and + - t = 0. Match each entry in List-I to the correct entry in List-II and choose the correct option.

(P) → (2), (Q) → (1), (R) → (4), (S) → (5)
(P) → (2), (Q) → (4), (R) → (3), (S) → (5)
(P) → (2), (Q) → (1), (R) → (4), (S) → (3)
(P) → (5), (Q) → (4), (R) → (1), (S) → (3)

JEE Advanced 2025 Paper 1

Consider the vectors x= i+2 j+3 k, y=2 i+3 j+ k, z=3 i+ j+2 k. For two distinct positive real numbers and , define X= x+ y- z, Y= y+ z- x, Z= z+ x- y. If the vectors X, Y, and Z lie in a plane, then the value of + -3 is .

JEE Advanced 2025 Paper 2

Let OP= -1 i+ j+ k, OQ= i+ -1 j+ k and OR= i+ j+ 12 k be three vectors, where , R-\0\ and O denotes the origin. If ( OP OQ ) OR=0 and the point ( , ,2) lies on the plane 3x+3y-z+l=0, then the value of l is .

JEE Advanced 2024 Paper 1

Let p=2 i+ j+3 k and q= i- j+ k. If for some real numbers , , and , we have 15 i+10 j+6 k= (2 p+ q )+ ( p-2 q )+ ( p q ), then the value of is .

JEE Advanced 2024 Paper 2

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 Advanced Mathematics chapters

Class 11Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Conic Sections Limits and Derivatives Statistics

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)