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Vector Algebra

JEE Main 2024 (Online) 29th January Evening ShiftMCQMedium📈 Topic in 36% papers+4−1
Ques. 1JEE Main 2024, 29 January (Evening Shift)

Let a unit vector u=x i+y j+z k make angles 2, 3 and 2 3 with the vectors 1 2 i+ 1 2 k, 1 2 j+ 1 2 k and 1 2 i+ 1 2 j respectively. If v= 1 2 i+ 1 2 j+ 1 2 k then | u- v|2 is equal to

  1. 112
  2. 52
  3. 7
  4. 9

Answer

(2) 52

Solution

∵ All three given vectors are unit vectors and | u|=1 ⇒ u p= (angle)

x+z 2= 2=0 x+z=0

y+z 2= 3= 12 y+z= 1 2

x+y 2= 2 3=- 12 x+y=- 1 2

Adding: x+y+z=0 y=0, z= 1 2, x=- 1 2

u- v=- 2 2 i- 1 2 j+0 k

| u- v|2=2+ 12= 52

Answer: (2)

Keep practising — Vector Algebra

Ques. 2JEE Main 2024, 29 January (Evening Shift)

Let OA= a, OB=12 a+4 b and OC= b, where O is the origin. If S is the parallelogram with adjacent sides OA and OC, then area of the quadrilateral OABCarea of S is equal to .

  1. 7
  2. 6
  3. 8
  4. 10
Ques. 3JEE Main 2024, 27 January (Morning Shift)

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

  1. 32
  2. 36
  3. 24
  4. 20
Ques. 4JEE Main 2024, 27 January (Morning Shift)

The least positive integral value of , for which the angle between the vectors i-2 j+2 k and i+2 j-2 k is acute, is .

Ques. 5JEE Main 2024, 27 January (Evening Shift)

The position vectors of the vertices A, B and C of a triangle are 2 i-3 j+3 k, 2 i+2 j+3 k and - i+ j+3 k respectively. Let l denote the length of the angle bisector AD of where D is on the line segment BC, then 2l2 equals :

  1. 45
  2. 50
  3. 42
  4. 49

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