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Vector Algebra

JEE Main 2025 (Online) 7th April Morning ShiftMCQEasy📈 Topic in 36% papers+4−1
Ques. 1JEE Main 2025, 7 April (Morning Shift)

Let the angle , 0 < < 2 between two unit vectors a and b be -1 ( 659 ). If the vector c = 3 a + 6 b + 9( a b), then the value of 9( c a) - 3( c b) is

  1. 31
  2. 29
  3. 24
  4. 27

Answer

(2) 29

Solution

= 659 = 1 - 6581 = 49 ( acute)

a b = 49, and ( a b) a = ( a b) b = 0

c a = 3 + 6 ( 49 ) = 3 + 83 = 173

c b = 3 ( 49 ) + 6 = 43 + 6 = 223

9( c a) - 3( c b) = 51 - 22 = 29

Answer: (2)

Keep practising — Vector Algebra

Ques. 2JEE 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 :

  1. 2 + 2
  2. 2 + 4 2
  3. 4 + 2 2
  4. 1 + 2
Ques. 3JEE 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

  1. 232
  2. 252
  3. 10
  4. 14
Ques. 4JEE 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. 5JEE 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. 6JEE 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. 7JEE 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 :

  1. 110
  2. 12
  3. 340
  4. 7 3
Ques. 8JEE 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. 1 155(-7 i + 9 j + 5 k)
  2. 1 155(-7 i + 9 j - 5 k)
  3. 1 155(7 i + 9 j - 5 k)
  4. 1 155(7 i + 9 j + 5 k)
Ques. 9JEE 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 :

  1. 15
  2. 18
  3. 12
  4. 9
Ques. 10JEE 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 :

  1. 77
  2. 154
  3. 308
  4. 462
Ques. 11JEE 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:

  1. 3
  2. 6
  3. - 6
  4. - 3

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