Sum of Two Vectors: Magnitude & Scalar Product

What are your thoughts on the subject?In summary, the conversation discusses the scenario where the magnitude of the sum of two vectors is less than the magnitude of either vector. It is concluded that in this case, the scalar product of the vectors must be negative. The conversation also mentions the equations V1+V2=V3 and A(dot)B=ABcos(θ) as relevant to the topic. The person asking the question is unsure of why the scalar product must be negative in this scenario.
  • #1
jdief
1
0

Homework Statement


If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:
-the vectors must be parallel and in the same direction
-the scalar product of the vectors must be negative
-none of these
-the scalar product of the vectors must be positive
-the vectors must be parallel and in opposite directions

Homework Equations


V1+V2=V3
A(dot)B=ABcos(θ)

The Attempt at a Solution


I know the answer is that the scalar product of the vectors must be negative, but I don't get why.
 
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  • #2


jdief said:

Homework Statement


If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:
-the vectors must be parallel and in the same direction
-the scalar product of the vectors must be negative
-none of these
-the scalar product of the vectors must be positive
-the vectors must be parallel and in opposite directions

Homework Equations


V1+V2=V3
A(dot)B=ABcos(θ)

The Attempt at a Solution


I know the answer is that the scalar product of the vectors must be negative, but I don't get why.
Hello jdief. Welcome to PF !

What have you tried?
 

1. What is the sum of two vectors?

The sum of two vectors is a new vector that results from adding the individual components of the two original vectors. This is known as vector addition and is represented by a single vector with a magnitude and direction that is equal to the combined magnitudes and directions of the original vectors.

2. How is the magnitude of a vector calculated?

The magnitude of a vector is calculated by taking the square root of the sum of the squared components of the vector. In other words, it is the length or size of the vector and is represented by a positive number.

3. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, such as temperature or time. A vector, on the other hand, has both magnitude and direction, such as force or velocity. In other words, a vector can be thought of as a combination of a scalar and a direction.

4. How do you calculate the scalar product of two vectors?

The scalar product of two vectors is also known as the dot product. It is calculated by multiplying the magnitudes of the two vectors and then multiplying that by the cosine of the angle between them. The resulting value is a scalar quantity.

5. What is the significance of the scalar product in physics?

The scalar product is used in physics to calculate the work done by a force, the power of a force, and the angle between two vectors. It also plays a role in determining the angle between two surfaces and calculating the potential energy of an object.

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