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Vectors Test - 9

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Vectors Test - 9
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  • Question 1
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    The unit vector in the direction of a given vector  

     

    Solution

     

     

     is called the unit vector of a given vector  

     

     

  • Question 2
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    Which of the following is a vector?

     

    Solution

     

     

    Acceleration is a vector quantity , because acceleration is defined as the rate of change of velocity w.r.t. time.

     

     

  • Question 3
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    Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.

     

    Solution

     

     

    Let position vector of point R be   . As point R divides externally the line segment PQ in the ratio 1:2 .therefore ,

    Also , mid point of the line segment RQ is : 
    Which is the position vector of point P.
    Therefore , P is the mid point of line segment RQ.

     

     

  • Question 4
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    Find the projection of the vector   on the vector

     

    Solution

     

     


    then projection of vector a on vector b is given by :

     

     

  • Question 5
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    If  θ is the angle between two vectors

     

    Solution

     

     


     

     

  • Question 6
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    Coinitial Vectors are

     

    Solution

     

     

    Two vectors whose initial point is same are called co- initial vectors

     

     

  • Question 7
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    In the figure which are the Equal vectors? 

     

    Solution

     

     

    are equal vectors , because they have equal magnitude and same direction.

     

     

  • Question 8
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    The scalar product of two nonzero vectors  

     

    Solution

     

     

    The scalar product of two nonzero vectors   by  

     

     

  • Question 9
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    Find   if for a unit vector  

     

    Solution

     

     

     

     

  • Question 10
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    If  θ is the angle between any two vectors   when θis equal to

     

    Solution

     

     


     

     

  • Question 11
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    Vectors A and BareCollinear

     

    Solution

     

     

    Two vectors A and B are said to be collinear , if they are parallel to the same line irrespective of their magnitudes and directions.

     

     

  • Question 12
    1 / -0.25

     

     

    Solution

     

     

     collinear vectors , because they are parallel in direction and having the same magnitude.

     

     

  • Question 13
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    The scalar product of two nonzero vectors  

     

    Solution

     

     

    The scalar product of two nonzero vectors  

     

     

  • Question 14
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    If    are unit vectors such that then, the value of   

     

    Solution

     

     


    It is given that :   are unit vectors such that  
    then :

     

     

  • Question 15
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    Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).

     

    Solution

     

     




    Therefore , the area of triangle  

     

     

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