Free Scalar Product MCQs with Answers

1. The scalar product of two vectors A and B is defined as

• 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 product of force and displacement, is a scalar. The sine form belongs to the vector product, whose result is a vector. The cosine factor is what makes the dot product zero for perpendicular vectors.

2. The scalar product of two perpendicular vectors is

• 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. It is also why no work is done by a force acting at right angles to the displacement, such as the centripetal force on a body in circular motion. The dot product is maximum when the vectors are parallel and negative when the angle exceeds 90 degrees.

3. For the vectors A equals 2i + 3j and B equals 4i minus j, the scalar product A dot B is

• 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. Only i with i and j with j contribute, because the unit vectors along different axes are perpendicular and their dot products vanish. The value 8 is the first term alone and 11 comes from adding rather than subtracting.

4. Which pair of quantities are both scalars?

• 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. Force, acceleration, velocity, momentum, torque and displacement are all vectors. The habit worth building is to ask whether reversing the direction changes the physical meaning, since for work it does not.