Free Scalar Product MCQs with Answers
29 Scalar Product MCQs from Physics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
The scalar product of two vectors is A dot B equals AB cos theta, producing a scalar determined by their magnitudes and included angle. Applications include work done and projection of one vector on another, with perpendicular vectors giving zero and the scalar product distinguished from the vector product.
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- A. AB sin theta, and the result is a vector
- B. AB cos theta, and the result is a scalar
- C. AB tan theta, and the result is a scalar
- D. AB, independent of the angle between them
Explanation: The dot product multiplies the magnitudes by the cosine of the angle between the vectors and gives a scalar, which is why work, the dot…
Correct answer: AB cos theta, and the result is a scalar- A. maximum
- B. equal to their magnitudes multiplied
- C. zero
- D. negative
Explanation: Cos 90 is zero, so the dot product vanishes whenever the vectors are at right angles, and this is the standard test for perpendicularity.
Correct answer: zero- A. 11
- B. 5
- C. 8
- D. minus 3
Explanation: In component form the dot product is the sum of the products of like components, so (2)(4) plus (3)(minus 1) gives 8 minus 3, which is 5.
Correct answer: 5- A. Force and acceleration
- B. Velocity and momentum
- C. Work and power
- D. Torque and displacement
Explanation: Work and power have magnitude only, with work being a dot product and power its rate of change with time.
Correct answer: Work and power- A. Displacement
- B. Speed
- C. Velocity
- D. Acceleration
Explanation: Speed is a scalar because it has magnitude only, whereas displacement, velocity and acceleration also require direction and are vectors.
Correct answer: Speed- A. 1
- B. i^
- C. j^
- D. k^
Explanation: Using the unit-vector cross-product rule, j x k = i, and therefore i·(j x k) = i·i = 1.
Correct answer: 1- A. A.B = A^ B^
- B. |A| = |B|
- C. |A^| = |B^|
- D. AB^ = BA^
Explanation: If A and B are equal vectors, then their magnitudes and unit vectors are equal, and A B-hat = B A-hat also remains equal.
Correct answer: A.B = A^ B^- A. A.B/A
- B. A.B/B
- C. A.cosθ
- D. Both a and b are correct
Explanation: The scalar projection of B on A is the component of B along the direction of A, given by A · B divided by the magnitude of A, written here…
Correct answer: A.B/A- A. A. B = Ax Bx + Ay By + Az Bz
- B. A. B = Ax By + Ay Bz + Az By
- C. A. B = Ay Bz + Az By + Az Bx
- D. A. B = Ax Bz + Ay By + Az Bx
Explanation: The dot product multiplies corresponding components and then adds them: A · B = AxBx + AyBy + AzBz.
Correct answer: A. B = Ax Bx + Ay By + Az Bz- A. 0
- B. 1
- C. -1
- D. i^
Explanation: Using the unit-vector cross-product rule, j × k = i. Hence i · (j × k) = i · i = 1, because the dot product of a unit vector with itself…
Correct answer: 1- 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|cosθScalar Product MCQs: common questions
Are these Scalar Product MCQs free?
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There are 29 Scalar Product MCQs in the Physics bank, shown 20 to a page with the correct answer and an explanation on each.
Does every Scalar Product MCQ have an explanation?
Yes. Each Scalar Product question shows the correct option and a written explanation of why it is correct, so a wrong answer teaches you something rather than just being marked wrong.
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