Free Vectors and Equilibrium MCQs with Answers
431 Vectors and Equilibrium MCQs from Physics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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Read the Vectors and Equilibrium notesFree MDCAT chapter notes with key terms431 questions · page 5 of 22
- A. 10N
- B. 1.366N
- C. 13.66N
- D. 136.6N
Explanation: To find the x-component of the resultant force when two forces of 10N magnitude are inclined at 30° and 60° with the x-axis, we need to…
Correct answer: 13.66N- A. 0
- B. 1/√2 (i - j)
- C. 1/√2 (i + j)
- D. (i - j)/2
Explanation: Let A= (i + j) and B=(i - j). The unit vector of A = i + j / |(i + j)||(i + j)|= √12+12=2 so, the unit vector of (i + j) = i + j /√2 =…
Correct answer: 0- A. 23
- B. -23
- C. 0
- D. 19
Explanation: To find the dot product (scalar product) of vectors A and B, you multiply the corresponding components and add them together:A · B = Ax_Bx…
Correct answer: 23- A. 0 ... 1
- B. 1 ... 0
- C. 0 ... 0
- D. 1 ... 1
Explanation: The dot product of two vectors A and B is given by A.B = |A||B| cosθ. If the angle θ between the vectors is 0°, cosθ = 1, so a vector…
Correct answer: 1 ... 0- A. 7/3
- B. 16/3
- C. 3/7
- D. 9/7
- E. 5/9
Explanation: Vector Y is in 4th xy quadrantY = √(4^2 + 6^2 + 12^2)Y = √(16 + 36 + 144)Y = √196Y = 14 (Y.Z)/Y = ( 4*2 + 6*4 + 12*4)/14 = 80/14 = 5.7 =…
Correct answer: 16/3- A. 11.77
- B. 22.99
- C. 55.77
- D. 77.81
- E. 99.18
Explanation: S.R = lSl lRl cos (theta) 13.5=(4)(6) cos (theta) Cos -1 (13.5/24) =theta Theta= 55.77 So, option C is correct.
Correct answer: 55.77- A. A scalar is multiplied by a scalar
- B. A scalar is multiplied by vector
- C. Two vectors are multiplied to give a scalar
- D. Sum of two scalars is taken
Explanation: The correct answer is Option C:Two vectors are multiplied to give a scalar.
Correct answer: Two vectors are multiplied to give a scalar- A. zero
- B. AB
- C. -AB
- D. A/b
- E. none
Explanation: The dot product of two vectors A and B is given by the formula A·B = |A| |B| cos(θ), where θ is the angle between the vectors.
Correct answer: AB- A. 0
- B. 45
- C. 60
- D. 90
Explanation: Dot product of two vectors is obtained by multiplying their magnitudes and the cos of angle between them.
Correct answer: 90- A. A B sin θ
- B. AB
- C. AB cos θ
- D. AB sec θ
Explanation: The scalar product, also known as the dot product, of two vectors A and B is calculated as |A||B| cos θ, where θ is the angle between the…
Correct answer: AB cos θ- A. Either of two vectors is a null vector
- B. Both of the vectors are null vectors
- C. The vectors are mutually perpendicular
- D. All of the above
Explanation: The correct option is (d) - if A.B = 0, we can conclude that all of the options are true.
Correct answer: All of the above- A. A cos θ
- B. |B|/|A|
- C. |B|/θ
- D. |B|cosθ
Explanation: The projection of vector B onto vector A is calculated using the formula |B|cosθ, where θ is the angle between the two vectors.
Correct answer: |B|cosθ- A. Not equal to the product of magnitudes of
- B. In the plane parallel to
- C. Perpendicular to the plane containing
- D. Less in magnitude than the product of magnitudes of
Explanation: The vector product, or cross product, of two vectors A and B results in a vector perpendicular to the plane containing A and B.
Correct answer: Perpendicular to the plane containing- A. 2i + 3j + 4k
- B. i+5j + 2k
- C. -142+7k
- D. 2i+5j+4k
Explanation: IT is incorrect as it shows the vector A. It represents the vector b {i+5j+2k}
Correct answer: i+5j + 2k- A. Unity
- B. Zero
- C. 90°
- D. Depends on the vector
Explanation: The vector product, or cross product, of a vector with itself is always zero.
Correct answer: Zero- A. Parallel
- B. Perpendicular
- C. Y-axis
- D. X- axis
Explanation: The vector product of two vectors is a vector perpendicular to both of them.
Correct answer: Perpendicular- A. They are parallel vectors
- B. They are anti-parallel vectors
- C. They are perpendicular vectors
- D. They are rotated through 270°
Explanation: The cross-product of two vectors, A and B, is defined as a vector that is perpendicular to both A and B, with a magnitude given by…
Correct answer: They are rotated through 270°- A. A
- B. 1
- C. 2A
- D. Zero
Explanation: The cross product of vector A with itself, denoted as A x A, is equal to zero.
Correct answer: Zero- A. Linear momentum
- B. Angular momentum
- C. Force
- D. Electric flux
Explanation: Angular momentum is an example of a vector product of two vectors. The vector product, also known as cross product, is an operation…
Correct answer: Angular momentum- A. √(12/7) (2i + 3j - k)
- B. √(7/12) (4i + 2j - 2k)
- C. √(7/12) (2i + 3j + k)
- D. √(3/5) (i + 2j - 3k)
- E. √(5/12) (3i + 5j - 2k)
Explanation: The magnitude of B is equal to √(4)² + (2)² + (2)²=√24The magnitude of A is equal to √(2)² + (3)² + (1)² =√14The parallel vector is…
Correct answer: √(12/7) (2i + 3j - k)