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CBSE Class 12 Mathematics Vector Algebra Extra Questions

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CBSE Class 12 Mathematics Vector Algebra Extra Questions. myCBSEguide has just released Chapter Wise Question Answers for class 12 Maths. There chapter wise Practice Questions with complete solutions are available for download in myCBSEguide website and mobile app. These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years. There are around 4-5 set of solved Chapter 10 Vector Algebra Mathematics Extra Questions from each and every chapter. The students will not miss any concept in these Chapter wise question that are specially designed to tackle Board Exam. We have taken care of every single concept given in CBSE Class 12 Mathematics syllabus and questions are framed as per the latest marking scheme and blue print issued by CBSE for class 12.

Class 12 Chapter 10 Maths Extra Questions

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Vector Algebra Extra Questions Class 12 Maths

Chapter 10 Vector Algebra


  1. Find the angle between two vectors a and b with magnitudes 3 and 2, respectively, having a.b=6.

    1. π5
    2. π3
    3. π2
    4. π4
  2. Find the angle between two vectors ˆi2ˆj+3ˆkand 3ˆi2ˆj+ˆk.

    1. cos1(47)
    2. cos1(67)
    3. cos1(59)
    4. cos1(57)
  3. Vector has

    1. direction
    2. None of these
    3. magnitude
    4. magnitude as well as direction
  4. Find the sum of the vectorsa=ˆi2ˆj+ˆk,b=2ˆi+4ˆj+5ˆk and c=ˆi6ˆj7ˆk.

    1. ˆi+4ˆjˆk
    2. 4ˆjˆk
    3. ˆi4ˆjˆk
    4. ˆi4ˆjˆk
  5. Find the direction cosines of the vector ˆi+2ˆj+3ˆk.

    1. 114,214,314
    2. 114,214,314
    3. 114,214,314
    4. 114,214,314
  6. The values of k which |ka|<|a| and ka+12a is parallel to a holds true are ________.
  7. If r.a=0r.b=0, and r.c=0 for some non-zero vector r, then the value of a(b×c) is ________.
  8. The angle between two vectors a and b with magnitudes 3 and 4, respectively, a.b = 23 is ________.
  9. Find a×b if a=2ˆi+ˆj+3ˆk,b=3ˆi+5ˆj2ˆk.

  10. Find the projection of a on b, if ab=8 and b=2ˆi+6ˆj+3ˆk.

  11. a Is unit vector and (xa)(x+a)=8, Then find |x|.

  12. Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q(4,1, – 2)

  13. Find sine of the angle between the vectors. a=2ˆiˆj+3ˆk,b=ˆi+3ˆj+2ˆk.

  14. Find the projection of the vector ˆi+3ˆj+7ˆk on the vector 7ˆiˆj+8ˆk

  15. Let a=ˆi+ˆj+ˆk,b=4ˆi2ˆj+3ˆk and c=ˆi2ˆj+ˆk.Find a vector of magnitude 6 units, which is parallel to the vector 2ab+3c.

  16. Let a=ˆi+4ˆj+2ˆk,b=3ˆi2ˆj+7ˆk and c=2ˆiˆj+4ˆk .Find a vector d which is perpendicular to both a and b and c.d=15.

  17. A girl walks 4 km towards west, then she walks 3 km in a direction 300 east of north and stops. Determine the girl’s displacement from her initial point of departure.

  18. Find a vector d which is to both a and b and c. d=15 Let a=ˆi+4ˆj+2ˆk,b=3ˆi2ˆj+7ˆk and c=2ˆiˆj+4ˆk.

Chapter 10 Vector Algebra


Solution

    1. π4Explanation: |a|=3,|b|=2,a.b=6
      a.b=|a|.|b|cosθ6
      =23cosθ
      cosθ=12θ=π4
    1. cos1(57)Explanation: a=ˆi2ˆj+3ˆk,b=3ˆi2ˆj+ˆk|a|=14,|b|=14,a.b=10
      a.b|a||b|=cosθ1014=cosθ
      cosθ=57θ=cos157
    1. magnitude as well as direction, Explanation: A vector has both magnitude as well as direction.
    1. 4ˆjˆkExplanation: We have: vectors a=ˆi2ˆj+ˆk, b=2ˆi+4ˆj+5ˆk and 
    1. 114,214,314Explanation: Let a=ˆi+2ˆj+3ˆk,Then, ˆa=a|a|=ˆi+2ˆj+3ˆk12+22+32=ˆi+2ˆj+3ˆk14
      Therefore , the D.C.’s of vector a are :
      114,214,314.
  1.  ]-1, 1 [k  12
  2. 0
  3. π3
  4. a×b=|ˆiˆjˆk213352|
    =ˆi(215)ˆj(49)+ˆk(103)
    =17ˆi+13ˆj+7ˆk
  5. We are given that, ab=8 and b=2ˆi+6ˆj+3ˆk
    The projection of a on b is given as = ab|b|
    =822+62+32
    =84+36+9
    =849=87
  6. |a|=1
    (xa).(x+a)=8
    |x|2|a|2=8
    |x|21=8
    |x|2=9
    |x|=3
  7. Given: Point P (2, 3, 4) and Q(4,1, – 2)
    Position vector of point P is a=2ˆi+3ˆj+4ˆk
    And Position vector of point Q is b=4ˆi+ˆj2ˆk
    And Position vector of mid-point R of PQ is a+b2=2ˆi+3ˆj+4ˆk+4ˆi+ˆj2ˆk2
    =6ˆi+4ˆj+2ˆk2=3ˆi+2ˆj+ˆk
  8. a×b=|ˆiˆjˆk213132|
    =11ˆiˆj+7ˆk
    |a×b|=(11)2+(1)2+(7)2
    =171=319
    sinθ=|a×b||a||b|=31914.14=31419
  9. Let a=ˆi+3ˆj+7ˆk and b=7ˆiˆj+8ˆk
    Projection of vector a on b=a.b|b|
    =(1)(7)+(3)(1)+7(8)(7)2+(1)2+(8)2
    =73+5649+61+64=60114
  10. According to the question ,
    a=ˆi+ˆj+ˆk,
    b=4ˆi2ˆj+3ˆk and
    c=ˆi2ˆj+ˆk
    Now ,2ab+3c
    =2(ˆi+ˆj+ˆk)(4ˆi2ˆj+3ˆk)+3(ˆi2ˆj+ˆk)
    =2ˆi+2ˆj+2ˆk4ˆi+2ˆj3ˆk+3ˆi6ˆj+3ˆk
    =ˆi2ˆj+2ˆk
    2ab+3c=ˆi2ˆj+2ˆk
    Now, a unit vector in the direction of vector is 2ab+3c=2ab+3c|2ab+3c|
    =ˆi2ˆj+2ˆk(1)2+(2)2+(2)2
    =ˆi2ˆj+2ˆk9
    =ˆi2ˆj+2ˆk3
    =13ˆi23ˆj+23ˆk
    Vector of magnitude 6 units parallel to the vector is ,
    =6(13ˆi23ˆj+23ˆk)
    =2ˆi4ˆj+4ˆk
  11. Given: Vectors a=ˆi+4ˆj+2ˆk and b=3ˆi2ˆj+7ˆk
    We know that the cross-product of two vectors, a×b is a vector perpendicular to both a and b
    Hence, vector d which is also perpendicular to both a and b is d=λ(a×b) where λ=1 or some other scalar.
    Therefore, d=λ|ijk142327|
    =λ[ˆi(28+4)ˆj(76)+ˆk(212)]
    d=32λˆiλˆj14λˆk…(i)
    Now given c=2ˆiˆj+4ˆk and c.d=15
    c.d=15
    =2(32λ)+(1)(λ)+4(14λ)=15
    64λ+λ56λ=15
    9λ=15
    λ=159
    λ=53
    Putting λ=53 in eq. (i), we get
    d=53[32ˆiˆj14ˆk]
    d=13[160ˆi5ˆj70ˆk]
  12. Let the initial point of departure is origin (0, 0) and the girl walks a distance OA = 4 km towards west.
    Through the point A, draw a line AQ parallel to a line OP, which is 300 East of North, i.e., in East-North quadrant making an angle of 300 with North.
    Again, let the girl walks a distance AB = 3 km along this direction OQ
    OA=4(i)=4ˆi …(i) [ Vector OA is along OX’] CBSE Class 12 Mathematics Vector Algebra Extra Questions
    Now, draw BM perpendicular to x – axis.
    In ΔAMB by Triangle Law of Addition of vectors,
    AB=AM+MB=(AM)ˆi+(MB)ˆi
    Dividing and multiplying by AB in R.H.S.,
    AB=ABAMABˆi+ABMBABˆj =3cos60oˆi+3sin60oˆj
    AB=312ˆi+332ˆi=32ˆi+332j …(ii)
    Girl’s displacement from her initial point O of departure to final point B,
    OB=OA+AB =4ˆi+(32ˆi+322ˆj) =(4+32)ˆi+332ˆj
    OB=52ˆi+332ˆj
  13. a=ˆi+4ˆj+2ˆk,b=3ˆi2ˆj+7ˆk and c=2ˆiˆj+4ˆk
    Let d=xˆi+yˆj+zˆk
    ATQ, d.a=0,d.b=0 and c.d=15, then,
    x + 4y + 2z = 0 …(1)
    3x – 2y + 7z = 0 …(2)
    2x – y + 4z = 15 …(3)
    On solving equation (1) and (2)
    CBSE Class 12 Mathematics Vector Algebra Extra Questions
    x28+4=y67=z212=k
    x = 32k, y = -k, z = -14k
    Put x, y, z in equation (3)
    2(32k) – (-k) + 4(-14k) = 15
    64k + k – 56k = 15
    9k = 15
    k=159
    k=53
    x=32×53=1603
    y=53
    z=14×53=703
    d=1603ˆi53ˆj703ˆk

Chapter Wise Important Questions Class 12 Maths Part I and Part II

  1. Relations and Functions
  2. Inverse Trigonometric Functions
  3. Matrices
  4. Determinants
  5. Continuity and Differentiability
  6. Application of Derivatives
  7. Integrals
  8. Application of Integrals
  9. Differential Equations
  10. Vector Algebra
  11. Three Dimensional Geometry
  12. Linear Programming
  13. Probability
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