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Vector Algebra Test - 1

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Vector Algebra Test - 1
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Weekly Quiz Competition
  • Question 1
    2 / -0.83

    Vector has

    Solution

    A vector has both magnitude as well as direction.

  • Question 2
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    Correct form of distributive law is

    Solution

    Distributive law is given by : 

  • Question 3
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    Magnitude of the vector  

    Solution

    We have :

  • Question 4
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    Find the unit vector in the direction of vector  where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively

    Solution



  • Question 5
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    If   is a non zero vector of magnitude ‘a ’and  λ a non zero scalar, then  λis a unit vector if

    Solution

  • Question 6
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    Find the values of x and y so that the vectors  are equal

    Solution

  • Question 7
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    If  P1 (x1 , y1 , z1 ) and  P2 (x2 , y2 , z2 ) are any two points, then the vector joining P1 and  P2is the vector P1P2. Magnitude of the vector  

    Solution

    If  P1 (x1 , y1 , z1 ) and  P2 (x2 , y2 , z2 ) are any two points, then the vector joining P1 and  P2is the vector P1P2, then ;

  • Question 8
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    Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7). 

    Solution

    The scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7) is given by : (- 5 –2) i.e. –7 and (7 –1) i.e. 6. Therefore, the scalar components are –7 and 6 .,and vector components are  

  • Question 9
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    Find a vector in the direction of the vector  which has a magnitude of 8 units

    Solution





  • Question 10
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    Find   , if     and   

    Solution


  • Question 11
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    Direction angles are angles

    Solution

    α,β,γare the angles which the position vector   makes with the positive x-axis ,y-axis and z-axis respectively are called direction angles.

  • Question 12
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     are any three vectors then the correct expression for distributivity of scalar product over addition is

    Solution

     are any three vectors then the correct expression for distributivity of scalar product over addition is :

  • Question 13
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    Find the values of x and y so that the vectors  

    Solution

  • Question 14
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    Find the direction cosines of the vector  

    Solution



  • Question 15
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    Solution

  • Question 16
    2 / -0.83

    Direction cosines

    Solution

    Cosines of the angles  α,β,γare called direction cosines.

  • Question 17
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    Magnitude of the vector  

    Solution

    We have : 

  • Question 18
    2 / -0.83

    Find the sum of the vectors      and   

    Solution

    We have: 

  • Question 19
    2 / -0.83

    Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

    Solution









    Therefore, the D.C.’s of vector AB are given by: 

  • Question 20
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    If a unit vector makes angles π/3 with    and an acute angle θwith  then find  θ

    Solution





  • Question 21
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    If l, m and n are direction cosines of the position vector OP the coordinates of P are

    Solution

    If l , m and n are the direction cosines of vector  then , the coordinates of point P are given by : lr ,mr and nr respectively.

  • Question 22
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    Unit vectors along the axes OX, OY and OZ are denoted by  

    Solution

    represents the unit vectors along the co ordinate axis i.e. OX ,OY and OZ respectively.

  • Question 23
    2 / -0.83

    Write down a unit vector in XY-plane, making an angle of 30 °with the positive direction of x-axis.

    Solution

  • Question 24
    2 / -0.83

    Find the angle between two vectors   with magnitudes and 2, respectively, having  

    Solution

     

  • Question 25
    2 / -0.83

    If a unit vector   makes angles and an acute angle θwith , then the components of   are

    Solution

    Let    It is given that left| , then , 





    Putting these values in (1) , we get : 



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