Cartesian Vectors MCQ

Test your knowledge with important Cartesian Vectors MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Cartesian Vectors MCQs at Bissoy

• A vector can always have_____________
  ক

  Only one component along any of the axis

  খ

  Only two components along any of the axis

  গ

  Only three components along any of the axis

  ঘ

  A unit vector along the direction perpendicular to its direction
• Which is true for the vector provided the only position coordinates given?
  ক

  (Final position coordinates + initial positions coordinates) gives the vector form of the vector

  খ

  (Final position coordinates – initial positions coordinates) gives the vector form of the vector

  গ

  (Initial positions coordinates – Final position coordinates) gives the vector form of the vector

  ঘ

  (Initial positions coordinates + Final position coordinates) gives the vector form of the vector
• What if we multiply a scalar to the unit vector?
  ক

  The direction will change accordingly

  খ

  The magnitude will change accordingly

  গ

  The magnitude will not change accordingly

  ঘ

  The direction will change by a factor of square root of the scalar
• What is the difference between a position vector and unit vector?
  ক

  Position vector has magnitude = 1 and direction, while the unit vector has magnitude = 0 and no direction

  খ

  Position vector has magnitude = 0 and direction, while unit vector has magnitude = 0 and no direction

  গ

  Position vector has some magnitude and direction, while the unit vector has magnitude = 0 and no direction

  ঘ

  Position vector has some magnitude and direction, while the unit vector has magnitude = 1 and a specified direction
• What is the magnitude of the unit vector?
  ক

  √3

  খ

  √2

  গ

  1

  ঘ

  0
• Three vectors emerging from a point are always in a single plane.
  ক

  True

  খ

  False
• Two vectors emerging from a point are always in a single plane.
  ক

  True

  খ

  False
• The value cos-1(-3/7) + cos-1(2/7) + cos-1(6/7) is ____________
  ক

  215.4˚

  খ

  273.4˚

  গ

  188.4˚

  ঘ

  219.4˚
• A force vector is along 4i – 4k direction and has a magnitude 100N and another force vector is along 4i +2j -4k and has a magnitude of 120N. What is the resultant of both forces?
  ক

  80i + 40j – 80k N

  খ

  80i – 40j – 80k N

  গ

  151i + 40j – 80k N

  ঘ

  151i+ 40j – 151k N
• The coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?
  ক

  -557i + 482j + 139k N

  খ

  -557i – 482j + 139k N

  গ

  -557i + 482j – 139k N

  ঘ

  557i – 482j – 139k N
• The coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). What are its directions?
  ক

  -0.742i + 0.643j + 0.186k

  খ

  0.742i – 0.643j – 0.186k

  গ

  -0.742i – 0.643j + 0.186k

  ঘ

  -0.742i + 0.643j – 0.186k
• What is the magnitude of the vector, 12i – 8j – 24k?
  ক

  18

  খ

  28

  গ

  38

  ঘ

  48
• In the figure given below, with F1 = 60j + 80k and F2= 50i -100j + 100k, what is the value of β? (β is the angle made by the resultant vector with the y-axis )
  ক

  76˚

  খ

  102˚

  গ

  19˚

  ঘ

  130˚
• Express the vector in the Cartesian Form, if the angle made by it with y and z axis is 60˚ and 45˚ respectively. Also, it makes an angle of α with the x-axis. The magnitude of the force is 200N.
  ক

  100i + 100j + 141.4k N

  খ

  100i – 100j + 141.4k N

  গ

  100i + 100j – 141.4k N

  ঘ

  100i – 100j – 141.4k N
• Find the angle α, for the vector making an angle by y and z axis as 60˚ and 45˚ respectively. It makes an angle of α with x-axis. The magnitude of the force is 200N.
  ক

  60˚

  খ

  120˚

  গ

  45˚

  ঘ

  90˚
• Which is true?
  ক

  ∑F = ∑Fx + ∑Fy + ∑Fz

  খ

  ∑F = -(∑Fx + ∑Fy + ∑Fz)

  গ

  ∑F = ∑Fxi + ∑Fyj + ∑Fzk

  ঘ

  ∑F = -(∑Fxi+ ∑Fyj + ∑Fzk)
• Which statement is correct about the vector F?
  ক

  F= Fcos β + Fcos α + Fcosγ

  খ

  F= Fsin β + Fcos α + Fcosγ

  গ

  F= Fcos β + Fsin α + Fcosγ

  ঘ

  F= Fcos β + Fcos α + Fsinγ
• For a vector F, Fcosβ is equal to zero. What does this refer?
  ক

  X-axis component is zero

  খ

  Y-axis component is zero

  গ

  Z-axis component is zero

  ঘ

  β = 180˚
• We can add the force vectors directly. But with dividing each by it’s magnitude first.
  ক

  True

  খ

  False
• What is the x-axis component of the force vector Ai + Bj +Ck with magnitude equal to F?
  ক

  B

  খ

  C

  গ

  Fcosα

  ঘ

  Fcosβ
• What is the sum of squares of the cosine angles made by the force vector with the coordinate axis?
  ক

  1

  খ

  ½

  গ

  2

  ঘ

  3
• What is cosα for force vector F = Ax + By +Cz (Given α, β and γ are the angles made by the vector with x, y and z axis respectively)?
  ক

  B/F

  খ

  C/F

  গ

  A/F

  ঘ

  1
• What is the magnitude of the Cartesian vector having the x, y and z axis components to be A, B and C?
  ক

  Square root of the squares each A, B and C

  খ

  Square of the squares each A, B and C

  গ

  Cube root of the squares each A, B and C

  ঘ

  Cube of the squares each A, B and C
• Which statement is right for force vector F = Ai + Bj + Ck?
  ক

  In rectangular components representation of any vector we have vector F = Ai + Bj + Ck

  খ

  In rectangular components representation of any vector we have vector F = Ax + By + Cz

  গ

  In rectangular components representation of any vector we have vector F = Fx + Fy + Fz

  ঘ

  In rectangular components representation of any vector we have vector F = Fi + Fj + Fk
• If the force vector F is having its x-axis component being equal to Z N, y-axis component be X N and z-axis component be Y N then vector F is best represented by?
  ক

  Xi + Yj + Zk

  খ

  Yi + Xj + Zk

  গ

  Zi + Yj + Xk

  ঘ

  Zi + Xj + Yk
• If A is any vector with Ai + Bj + Ck then what is the y-axis component of the vector?
  ক

  B units

  খ

  A units

  গ

  C units

  ঘ

  Square root of a sum of squares of the three, i.e. A, B and C
• In right handed coordinate system which axis is considered to be positive?
  ক

  The thumb is z-axis, fingers curled from x-axis to y-axis

  খ

  The thumb is x-axis, fingers curled from z-axis to y-axis

  গ

  The thumb is y-axis, fingers curled from x-axis to z-axis

  ঘ

  The thumb is z-axis, fingers curled from y-axis to x-axis