Vector Algebra

JEE Main 2025 (Online) 7th April Evening ShiftMCQMedium📈 Topic in 37% papers+4−1

Ques. 1JEE Main 2025, 7 April (Evening Shift)

Let a and b be the vectors of the same magnitude such that | a + b| + | a - b|| a + b| - | a - b| = 2 + 1. Then | a + b|2| a|2 is :

2 + 2
2 + 4 2
4 + 2 2
1 + 2

Answer

(1) 2 + 2

Solution

Let | a + b| = p, | a - b| = q and | a| = | b| = r.

By componendo–dividendo, p + qp - q = 2 + 1

pq = ( 2 + 1) + 1( 2 + 1) - 1 = 2 + 2 2 = 1 + 2

p2 = (1 + 2)2 q2 = (3 + 2 2) q2

Also p2 + q2 = 2| a|2 + 2| b|2 = 4r2

(4 + 2 2) q2 = 4r2 q2 = 4r24 + 2 2 = 2r22 + 2

p2r2 = 2(3 + 2 2)2 + 2 = 2(3 + 2 2)(2 - 2)2

= 6 - 3 2 + 4 2 - 4 = 2 + 2

Answer: (1)

Keep practising — Vector Algebra

Ques. 2JEE Main 2025, 4 April (Morning Shift)

Consider two vectors u = 3 i - j and v = 2 i + j - k, > 0. The angle between them is given by -1 ( 52 7 ). Let v = v1 + v2, where v1 is parallel to u and v2 is perpendicular to u. Then the value of | v1 |2 + | v2 |2 is equal to

Ques. 3JEE Main 2025, 4 April (Evening Shift)

Let the three sides of a triangle ABC be given by the vectors 2 i- j+ k, i-3 j-5 k and 3 i-4 j-4 k. Let G be the centroid of the triangle ABC. Then 6 (| AG|2+| BG|2+| CG|2 ) is equal to .

Ques. 4JEE Main 2025, 3 April (Morning Shift)

Let a = i + j + k, b = 3 i + 2 j - k, c = j + k and d be a unit vector such that a d = b d and c d = 1. If c is perpendicular to a, then |3 d + c|2 is equal to

Ques. 5JEE Main 2025, 3 April (Evening Shift)

Let a = i + 2 j + k, b = 3 i - 3 j + 3 k, c = 2 i - j + 2 k and d be a vector such that b d = c d and a d = 4. Then |( a d)|2 is equal to .

Ques. 6JEE Main 2025, 2 April (Morning Shift)

Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be 5, 6 and 7 square units respectively. Then the area (in square units) of the BCD is equal to :

Ques. 7JEE Main 2025, 2 April (Morning Shift)

If a is a nonzero vector such that its projections on the vectors 2 i - j + 2 k, i + 2 j - 2 k and k are equal, then a unit vector along a is :

1 155(-7 i + 9 j + 5 k)
1 155(-7 i + 9 j - 5 k)
1 155(7 i + 9 j - 5 k)
1 155(7 i + 9 j + 5 k)

Ques. 8JEE Main 2025, 2 April (Evening Shift)

Let a = 2 i - 3 j + k, b = 3 i + 2 j + 5 k and a vector c be such that ( a - c) b = -18 i - 3 j + 12 k and a c = 3. If b c = d, then | a d| is equal to :

Ques. 9JEE Main 2025, 29 January (Morning Shift)

Let a = 2 i - j + 3 k, b = 3 i - 5 j + k and c be a vector such that a c = c b and ( a + c) ( b + c) = 168. Then the maximum value of | c|2 is :

Ques. 10JEE Main 2025, 29 January (Evening Shift)

Let a be a unit vector perpendicular to the vectors b = i - 2 j + 3 k and c = 2 i + 3 j - k, and a makes an angle of -1 (- 13 ) with the vector i + j + k. If a makes an angle of 3 with the vector i + j + k, then the value of is:

Ques. 11JEE Main 2025, 28 January (Morning Shift)

Let a = i + j + k, b = 2 i + 2 j + k and d = a b. If c is a vector such that a c = | c|, | c - 2 a|2 = 8 and the angle between d and c is 4, then |10 - 3 b c| + | d c|2 is equal to .

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)