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Vectors Test - 6

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Vectors Test - 6
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  • Question 1
    1 / -0.25

    For what values of x and y, the vectorsare equal?

    Solution

    Two  vectors are  equal if their corresponding components are equal.
    Hence, 2x = 3
    or x = 3/2
    and 2x = y
    or y = 2 * 3/2
    y = 3

  • Question 2
    1 / -0.25

    Two or more vectors having the same initial point are called ​

    Solution

    Two or more vectors having the same initial point are called coinitial vectors.

  • Question 3
    1 / -0.25

    If   ,the vectors a and b are ______ .​

    Solution


    Both of these vectors are pointing the same direction but they have different magnitude. Hence, they are collinear vectors .
    Collinear Vectors Meaning

  • Question 4
    1 / -0.25

    If the magnitude of the position vector is 7, the value of x is:​

    Solution


    |a| = (x2  + 22  + (2x)2 )1/2
    7 = (x2 + 22 + (2x)2 )1/2
    ⇒49 = x2 + 22 + 4x2
    ⇒49 = 4 + 5x2
    ⇒5x2 = 45
    ⇒x2 = 9
    x = ±3

  • Question 5
    1 / -0.25

    If and  are the position vectors of the points A, B, C and D such that   then ABCD is:

    Solution

    Given:

    If we divide both sides with 2 we get,

    ⇒ Mid pt. of  AC = Mid. pt. of  BD
    ∴ABCD  is a parallelogram.

  • Question 6
    1 / -0.25

    If  , then

    Solution

    a = 2i + 3j - 6k
    |a| = √4+9+36 = √49 = 7
    b = 6i - 2j + 3k
    |b| = √36+4+9 = √49 = 7
    |a| = |b|
    Hence, option A is correct.

  • Question 7
    1 / -0.25

    What is the additive identity of a vector?​

    Solution

    In the Additive Identity of vectors, the additive identity is zero vector 0.
    For any vectorV additive identity is defined as,
    0 + V = V  and V + 0 = V

  • Question 8
    1 / -0.25

    The angles α, β, γmade by the vector  with the positive directions of X, Y and Z-axes respectively, then the direction cosines of the vector are: 

    Solution

    Direction Cosines for angle  α, β, γare:
    cos α, cos β, cos γ
    Direction Cosines and Direction Ratio of a Line | Definition, Examples,  Diagrams

  • Question 9
    1 / -0.25

    If a and b are the position vectors of two points A and B and C is a point on AB produced such that AC = 3AB, then position vector of C will be ​

    Solution

    Position vector of A = OA = a
    Position vector of B  = OB  = b
    Now, AC = OC - OA
    Also, AB = OB - OA
    Given, AC = 3AB
    ⇒OC - OA = 3(OB - OA)
    ⇒OC = 3b - 2a

  • Question 10
    1 / -0.25

    Vector of magnitude 1 is called.​

    Solution

    A vector whose magnitude (i.e., length) is equal to 1 is called a unit vector . There are exactly two unit vectors in any given direction and one is the negative of the other.

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