# Dot Product Rules Multiple choice

• Lothar
In summary, the conversation is about determining the validity of solutions for dot product multiplication and seeking help for understanding the concept. The person has found two of the solutions to be valid and two to be invalid, but is unsure about their reasoning. They are seeking clarification and are on their last submission. A hint is given to consider the type of quantity, vector or scalar, involved in dot product multiplication.
Lothar

## Homework Statement

See the image
http://tinypic.com/r/33z6vz5/7

## Homework Equations

The rules of dot product multiplication.

## The Attempt at a Solution

I've determined that 2 of the solutions are valid, while two of the choices are invalid. I thought C and D looked correct, making A and B incorrect. Unfortunately it wasn't so. I'm down to my last submission and I really don't know what I'm doing wrong.

Thanks you

Why do you think the answers are valid or invalid? You need reasons better than an answer "looked correct."

Hint: What type of quantity, vector or scalar, is the dot product of two vectors?

## 1. What is the dot product?

The dot product is a mathematical operation that takes two vectors and returns a single scalar value. It is also known as the scalar product or inner product.

## 2. How do you calculate the dot product?

The dot product is calculated by multiplying corresponding components of two vectors and then summing the products. In other words, the dot product of two vectors a and b is given by a · b = a1b1 + a2b2 + ... + anbn.

## 3. What are the properties of the dot product?

The dot product has several important properties, including commutativity, distributivity, and associativity. It is also related to the angle between two vectors through the cosine rule: a · b = |a||b|cosθ.

## 4. How is the dot product used in physics and engineering?

The dot product is used in physics and engineering to calculate work, power, and force. In mechanics, it can be used to determine the angle between two forces or the angle between a force and a displacement. It is also used in signal processing to measure the similarity between two signals.

## 5. How does the dot product relate to the cross product?

The dot product and the cross product are two different types of vector multiplication. While the dot product results in a scalar value, the cross product results in a vector. However, they are related through the identity a · (b × c) = 0, which means that the dot product of a vector and the cross product of two other vectors is equal to zero.

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