Self Studies
Self Studies
Self Studies
Self Studies
Selfstudy
Selfstudy

Vectors Test - 4

Result Self Studies

Vectors Test - 4
  • Score

    -

    out of -
  • Rank

    -

    out of -
TIME Taken - -
Self Studies

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Self Studies Self Studies
Weekly Quiz Competition
  • Question 1
    1 / -0
    If is a proper vector, then number of unit vectors collinear with is
    Solution
    Proper vector is a synonym of eigen vector and the number of collinear unit vectors is 2.
    Hence, if is a proper vector, then number of unit vectors collinear with is 2.
  • Question 2
    1 / -0
    If and are non-zero non-collinear vectors, then the number of unit vectors at right angles to both and is
    Solution
    Since and are non-zero non-collinear vectors, × is a non-zero vector at right angles to both and .
    Hence, are the two unit vectors perpendicular to both and .
  • Question 3
    1 / -0
    The vectors 2 + 3 - 6 and are perpendicular when
    Solution
    If two vectors a and b are perpendicular to each other, then





    Now, going by the options, a = 6, b = 2 and c = 3 satisfy the equation. Hence, option (3) is correct.
  • Question 4
    1 / -0
    If θ is the angle between vectors and , such that ≥ 0, then
    Solution
    0 ⇒ ab cos θ ≥ 0
    ⇒ cos θ ≥ 0 ⇒ 0 ≤
  • Question 5
    1 / -0
    The magnitude of the resultant of vectors and is
    Solution
    Let R be the magnitude of resultant of two vectors.

    Then



    Since

    Therefore,
  • Question 6
    1 / -0
    The unit vector in the direction of sum of the vectors and is
    Solution
    Sum of the given vectors
    =
    =
    Unit vector in the direction of the sum of the given vectors
    =
    =
  • Question 7
    1 / -0
    If are the vertices of an equilateral triangle whose orthocentre is at the origin, then
    Solution
    Since the triangle is equilateral, orthocentre coincides with the centroid.
    P.V. of orthocentre = P.V. of centroid =
  • Question 8
    1 / -0
    If I is the incentre of triangle ABC, then is equal to
    Solution
    Taking the incentre of the triangle (I) as origin, we have

  • Question 9
    1 / -0
    If and are unit vectors such that is at right angles to 7 , then the angle between and is
    Solution
    Given
    ⇒ = 0
    Þ 7 = 0
    Þ
    Þ cos θ = , θ being the angle between and
    Þ θ =
  • Question 10
    1 / -0
    If are three mutually perpendicular unit vectors then || is equal to
    Solution
    ||2 = () () ()
    = + +
    + 2 ( + + )
    = ||2 + ||2 + ||2 + 0
    (Q = = = 0 as are mutually orthogonal)
    = 12 + 12 + 12 = 3
    = || =
  • Question 11
    1 / -0
    If are mutually perpendicular vectors of equal magnitude, then the angle θ, which makes with any of these three vectors, is given by
    Solution
    Let || = || = || = k (say), then ||

    =

    =

    (Note that     )

    If θ is the angle between     and , then

    cos θ =

    cos θ =

    cos θ =     (∴ = 0)

    cos θ =

    ⇒ θ = cos-1
  • Question 12
    1 / -0
    If , and are linearly dependent vectors and || = , then which of the following is correct?
    Solution
    Since are linearly dependent, so they are coplanar.
    Hence, [] = 0
    ⇒ = 0
    ⇒ 3β - 4α - (4β - 4) + 4α - 3 = 0
    ⇒ -β = -1
    ⇒ β = 1
    Also, || =
    ⇒ ||2 = 3
    ⇒ 12 + α2 + β2 = 3
    ⇒ 1 + α2 + 1 = 3
    ⇒ α2 = 1
    ⇒ α = ±1
  • Question 13
    1 / -0
    Which of the following is not a vector quantity?
    Solution
    Mass is not a vector quantity.
    Vector Quantities: Vector quantities refer to the physical quantities characterized by the presence of both magnitude as well as direction. For example, displacement, force, torque, momentum, acceleration, velocity, etc.

    Scalar Quantities: The physical quantities which are specified with the magnitude or size alone are scalar quantities. For example, length, speed, work, mass, density, etc.
  • Question 14
    1 / -0
    A vector with magnitude zero is called a
    Solution
    A vector with magnitude zero is called a null vector.
  • Question 15
    1 / -0
    The magnitude of a vector can never be
    Solution
    Magnitude of a vector can never be negative, it's either 0 or positive.
  • Question 16
    1 / -0
    If is a non-zero vector, then is a
    Solution
    is a unit vector in the direction of , that is parallel to vector a.
  • Question 17
    1 / -0
    For any two vectors and , which of the following is true?
    Solution
    Using triangular inequality and the fact that vector a and vector b can be in the same straight line, || ≤ || + || is the only true result.
  • Question 18
    1 / -0
    If is a unit vector and is a non-zero vector not parallel to , then the vector is
    Solution


    =

    =
    Since dot product is 0, so the given vector is at right angle to vector a.
  • Question 19
    1 / -0
    If and is perpendicular to , then value of t is
    Solution
    For perpendicular of two vectors, dot product is zero.

    (    ) .= 0

    (1 - t) . 1 + (3 + t) . 1 + t . 0 = 0

    4 = 0,

    which cannot be true for any t ∈ R
  • Question 20
    1 / -0
    If and are the position vectors of A and B, respectively, then the position vector of a point C in AB produced, such that = 3 , is
    Solution
    = 3
    ⇒ )
    where = P.V. of C
    ⇒
  • Question 21
    1 / -0
    The vectors and are
    Solution
    In this case
  • Question 22
    1 / -0
    The three vectors and form
    Solution
    Let , and

    Vector a, b and c satisfy and

    Therefore, the given vectors form a right angled triangle.
  • Question 23
    1 / -0
    If = 0, then is a
    Solution
  • Question 24
    1 / -0
    If ABCDEF is a regular hexagon where = and = , then is equal to
    Solution


    Each of the triangles AOB, BOC and COD is an equilateral triangle, and O is the centre of the hexagon.
    Therefore, AOD = 180° and
    =
    (ABCO and BCDO are parallelograms.)
  • Question 25
    1 / -0
    In a triangle ABC, if D is the mid-point of side [BC], then find .
    Solution



    = 2
    = 2
    Or
    =
  • Question 26
    1 / -0
    Direction cosines of the vector are
    Solution
    Vector makes angles 0o, 90o and 90o respectively with +ve directions of x-axis, y-axis and z-axis. Hence direction cosines of i are
    < cos 0o, cos 90o, cos 90o . i.e. < 1, 0, 0 >
  • Question 27
    1 / -0
    Direction cosines of the vector are
    Solution

    Þ || = = 7
    Hence
    =
    Hence d.c. of are <>.
  • Question 28
    1 / -0
    Direction cosines of the vector are
    Solution
    Since ,
    Therefore, direction cosines of are:
    <>
  • Question 29
    1 / -0
    If (+ ) () = 0, then
    Solution
    () () = 0
    ⇒     - = 0
    ⇒ |     |2 = | |2
    ⇒ |     | = | |
  • Question 30
    1 / -0
    If and are vectors with components (-1, 2), (3, -2) and (0, 5), respectively, then equals
    Solution

    = (-1 + 3 -2 (0), 2 -2 -2(5))
    = (2, -10)
    =
Self Studies
User
Question Analysis

  • Correct -

  • Wrong -

  • Skipped -

My Perfomance
  • Score

    -

    out of -
  • Rank

    -

    out of -
Re-Attempt Weekly Quiz Competition
Self Studies Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Self Studies
Click on Allow to receive notifications
Allow Notification
Self Studies
Self Studies Self Studies
To enable notifications follow this 2 steps:
  • First Click on Secure Icon Self Studies
  • Second click on the toggle icon
Allow Notification
Get latest Exam Updates & FREE Study Material Alerts!
Self Studies ×
Open Now