Scalar Product Questions

A scalar quantity is a physical quantity with only magnitudes. A scalar product is an algebraic operation between two equal-length sequences of numbers and returns a single number.

A vector quantity is a physical quantity that has both magnitudes and directions. It is represented by a lowercase alphabet with a “hat” circumflex (“û“).

Scalar and vector are two ways of multiplying vectors.

It is represented by:

Vector product or cross product is a binary operation on two vectors in three-dimensional space.

The magnitude of the vector product can be represented as follows:

Read more: Scalar Product.

Important Scalar Product Questions with Answers

1. The scalar product indicates the way of _______ two different vectors.

1. Adding
2. Subtracting
3. Multiplying
4. Dividing

Answer: c) Multiplying

Explanation: The scalar product indicates the way of multiplying two different vectors.

2. Scalar product is also known as ______.

1. Inner product
2. Cross product
3. Dot product
4. Both a) and c)

Answer: d) Both a) and c)

Explanation: The Scalar product is also known as the inner product or dot product.

3. a.b = |a| |b| cosθ, this formula represents the _____.

1. Scalar product of two vectors
2. Vector product of two vectors

Answer: a) Scalar product of two vectors

Explanation: This formula represents the scalar product of two vectors.

4. Scalar multiplication is denoted by a ______.

1. Dash
2. Dot
3. Semicolon
4. Comma

Answer: b) Dot

Explanation: Scalar multiplication is always denoted by a dot, hence the name dot product.

5. 10 meters is a _____ quantity.

1. Scalar
2. Vector
3. Dimensionless
4. None of the options

Answer: a) Scalar

Explanation: 10 meters indicates only the magnitude and does not indicate any direction. Hence it is a scalar quantity.

6. The electric charge is a ______.

1. Scalar quantity
2. Vector quantity

Answer: a) Scalar quantity

Explanation: Electric charge is a scalar quantity since it has only magnitude and no direction.

7. Which among the following is a vector quantity?

1. Mass
2. Displacement
3. Temperature
4. Density

Answer: b) Displacement

Explanation: Displacement is a vector quantity among the above options.

8. Cross product is referred to as _____.

1. Scalar product
2. Vector product

Answer: b) Vector product

Explanation: Vector product is also known as the cross product.

9. What is the formula to represent the magnitude of the vector product?

The magnitude of the vector product is represented using the formula:

10. State true or false: Both scalar and vector quantities are measurable.

1. TRUE
2. FALSE
   

Answer: a) TRUE

Explanation: Both scalar and vector quantities possess magnitude, and hence they are measurable.

Practice Questions

1. What is a vector quantity?
2. What is a scalar quantity?
3. Explain the scalar product with an example.
4. Explain the vector product with an example.
5. List 5 scalar quantities.