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Vectors Test - 4

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Vectors Test - 4
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  • Question 1
    1 / -0.25

     

    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 2
    1 / -0.25

     

     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 3
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    Find the values of x and y so that the vectors  

     

    Solution

     

     

     

     

  • Question 4
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    Find the direction cosines of the vector  

     

    Solution

     

     



     

     

  • Question 5
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    Solution

     

     

     

     

  • Question 6
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    Direction cosines

     

    Solution

     

     

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

     

     

  • Question 7
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    Magnitude of the vector  

     

    Solution

     

     

    We have : 

     

     

  • Question 8
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    Find the sum of the vectors      and   

     

    Solution

     

     

    We have: 

     

     

  • Question 9
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    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 10
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    If a unit vector makes angles π/3 with    and an acute angle θwith  then find  θ

     

    Solution

     

     





     

     

  • Question 11
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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 12
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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 13
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    Write down a unit vector in XY-plane, making an angle of 30 °with the positive direction of x-axis.

     

    Solution

     

     

     

     

  • Question 14
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    Find the angle between two vectors   with magnitudes and 2, respectively, having  

     

    Solution

     

     


     

     

  • Question 15
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    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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