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Vector Algebra

JEE Main 2024 (Online) 4th April Morning ShiftMCQMedium📈 Topic in 36% papers+4−1
Ques. 1JEE Main 2024, 4 April (Morning Shift)

Let a unit vector which makes an angle of 60 with 2 i+2 j- k and an angle of 45 with i- k be C. Then C+ (- 12 i+ 13 2 j- 23 k ) is:

  1. - 23 i+ 23 j+ ( 12+ 2 23 ) k
  2. ( 1 3+ 12 ) i+ ( 1 3- 13 2 ) j+ ( 1 3+ 23 ) k
  3. 23 i- 12 k
  4. 23 i+ 13 2 j- 12 k

Answer

(3) 23 i- 12 k

Solution

Let C=a i+b j+c k, a2+b2+c2=1

C (2 i+2 j- k)=1 3 60 2a+2b-c= 32

C ( i- k)=1 2 45 a-c=1

c=a-1, b= 1-2a4; put in a2+b2+c2=1:

36a2-36a+1=0 a= 12 23, b= 13 2, c=- 12 23

Upper signs: C+ (- 12 i+ 13 2 j- 23 k )= 23 i+0 j- 12 k option (3)

(Lower signs give - 23 i+ 23 j- ( 12+ 2 23 ) k, which is not in the options.)

Answer: (3)

Keep practising — Vector Algebra

Ques. 2JEE Main 2024, 4 April (Morning Shift)

Let ABC be a triangle of area 15 2 and the vectors AB= i+2 j-7 k, BC=a i+b j+c k and AC=6 i+d j-2 k, d>0. Then the square of the length of the largest side of the triangle ABC is .

Ques. 3JEE Main 2024, 4 April (Evening Shift)

For > 0, let be the angle between the vectors a = i + j - 3 k and b = 3 i - j + 2 k. If the vectors a + b and a - b are mutually perpendicular, then the value of (14 )2 is equal to

  1. 25
  2. 50
  3. 20
  4. 40
Ques. 4JEE Main 2024, 4 April (Evening Shift)

Let a = i + j + k, b = 2 i + 4 j - 5 k and c = x i + 2 j + 3 k, x R. If d is the unit vector in the direction of b + c such that a d = 1, then ( a b) c is equal to

  1. 3
  2. 9
  3. 11
  4. 6
Ques. 5JEE Main 2024, 1 February (Morning Shift)

Let a=-5 i+ j-3 k, b= i+2 j-4 k and c=((( a b) i) i) i. Then c (- i+ j+ k) is equal to :

  1. -12
  2. -10
  3. -13
  4. -15
Ques. 6JEE Main 2024, 1 February (Evening Shift)

Consider a ABC where A(1,3,2), B(-2,8,0) and C(3,6,7). If the angle bisector of BAC meets the line BC at D, then the length of the projection of the vector AD on the vector AC is :

  1. 372 38
  2. 19
  3. 392 38
  4. 382
Ques. 7JEE Main 2024, 1 February (Evening Shift)

Let a= i+ j+ k, b=- i-8 j+2 k and c=4 i+c2 j+c3 k be three vectors such that b a= c a. If the angle between the vector c and the vector 3 i+4 j+ k is , then the greatest integer less than or equal to 2 is .

Ques. 8JEE Main 2024, 31 January (Morning Shift)

Let a=3 i+ j-2 k, b=4 i+ j+7 k and c= i-3 j+4 k be three vectors. If a vector p satisfies p b= c b and p a=0, then p ( i- j- k) is equal to

  1. 24
  2. 32
  3. 36
  4. 28
Ques. 9JEE Main 2024, 31 January (Morning Shift)

Let a and b be two vectors such that | a|=1, | b|=4, and a b=2. If c=(2 a b)-3 b and the angle between b and c is , then 192 2 is equal to .

Ques. 10JEE Main 2024, 31 January (Evening Shift)

Let a=3 i+2 j+ k, b=2 i- j+3 k and c be a vector such that ( a+ b) c=2( a b)+24 j-6 k and ( a- b+ i) c=-3. Then | c|2 is equal to .

Ques. 11JEE Main 2024, 30 January (Morning Shift)

Let a=a1 i+a2 j+a3 k and b=b1 i+b2 j+b3 k be two vectors such that | a|=1, a b=2 and | b|=4. If c=2( a b)-3 b, then the angle between b and c is equal to:

  1. -1 (- 1 3 )
  2. -1 ( 23 )
  3. -1 ( 2 3 )
  4. -1 (- 32 )

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