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Vector Algebra Test - 4

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Vector Algebra Test - 4
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Weekly Quiz Competition
  • Question 1
    2 / -0.83

    Zero Vector

    Solution

    A vector whose initial and terminal points coincides is called Zero Vector. The magnitude of Zero Vector is also Zero.

  • Question 2
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    If a vector is expressed in component form as  then the magnitude of the vector  is  

    Solution

  • Question 3
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    Find the value of x for which  x  is a unit vector

    Solution


  • Question 4
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    Find the angle between two vectors  

    Solution




  • Question 5
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    Find  λand μif  

    Solution


    It is given that: 



  • Question 6
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    Unit Vector is

    Solution

    The vector whose magnitude is always 1 or unity is called a Unit Vector.

  • Question 7
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    If a vector   is expressed in component form as  then x, y and z are referred to as

    Solution

    In  x , y and z represents the components of  along x-axis ,y-axis and z-axis respectively.

  • Question 8
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    Show that the points A(1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

    Solution



    Therefore , AB and BC are parallel, but point B is common , so points , A,B,C are collinear. As  

  • Question 9
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    Find the projection of the vector  

    Solution

  • Question 10
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    Let the vectors   be such that  is a unit vector if the angle between vectors  is  

    Solution


  • Question 11
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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 12
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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 13
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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 14
    2 / -0.83

    Find the projection of the vector   on the vector

    Solution


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

  • Question 15
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    If  θ is the angle between two vectors

    Solution


  • Question 16
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    Coinitial Vectors are

    Solution

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

  • Question 17
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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 18
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    The scalar product of two nonzero vectors  

    Solution

    The scalar product of two nonzero vectors   by  

  • Question 19
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    Find   if for a unit vector  

    Solution

  • Question 20
    2 / -0.83

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

    Solution


  • Question 21
    2 / -0.83

    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 22
    2 / -0.83

    Solution

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

  • Question 23
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    The scalar product of two nonzero vectors  

    Solution

    The scalar product of two nonzero vectors   : 

  • Question 24
    2 / -0.83

    If    are unit vectors such that then, the value of   

    Solution


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

  • Question 25
    2 / -0.83

    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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