# Calculating Vectors: A, B, and C

• organgeatom
In summary, the conversation is about a problem set involving vector operations. The person is stuck on some questions and is seeking help. The questions include finding the magnitude of vectors, adding and multiplying vectors, and calculating the angle between vectors. The expert suggests using basic vector properties and operations to solve the questions.
organgeatom

## Homework Statement

I cannot find other sources to help me with this problem set, I have A B and C vectors defined by: A (2,1,1) B(1,-1,0), C(-1,1,-1)
From these I have a list of questions and some I am stuck on are:each of these are vectors with an arrow above it
1. |A| + |B| this I did as √ax^2 +ay^2 +az^2 + √the same for B
2. |A + B| but how do i do this, what is the difference between these?

3. A + B

4. 3C

5. A dot (B X C)

8. What is the angle between A and B, A and C, and B and C? in radians use pi

id appreciate any help!

organgeatom said:
1. |A| + |B| this I did as √ax^2 +ay^2 +az^2 + √the same for B

This would be correct.

organgeatom said:
2. |A + B| but how do i do this, what is the difference between these?

This is asking for you the magnitude of (vector A + vector B), question 1 was asking you for the magnitude of vector A + the magnitude of vector B. Start by first calculating what A+B is, how do you add two vectors together?

organgeatom said:
3. A + B

The same as question 2.

organgeatom said:
4. 3C

Do you know how to multiply a vector by a scalar?

organgeatom said:
5. A dot (B X C)

Do you know the terms 'dot product' and 'cross-product'?

organgeatom said:
8. What is the angle between A and B, A and C, and B and C? in radians use pi

This question depends on if you can do question 5.

Wikipedia explains the basic properties of vectors such as addition, scalar multiplication, length as well as dot and cross products.

## 1. How do you calculate the magnitude of a vector?

The magnitude of a vector can be calculated by finding the square root of the sum of the squares of its components. In other words, the magnitude of vector A = √(Ax² + Ay² + Az²).

## 2. What is the difference between a position vector and a displacement vector?

A position vector describes the location of a point in space relative to a fixed origin, while a displacement vector describes the change in position from one point to another. In other words, a displacement vector has both magnitude and direction, while a position vector only has direction.

## 3. How do you add two vectors together?

To add two vectors, you must first break them down into their x, y, and z components. Then, add the components of each vector separately. The resulting vector will have the sum of the x components, the sum of the y components, and the sum of the z components.

## 4. What is the dot product of two vectors?

The dot product of two vectors is a scalar value equal to the product of their magnitudes and the cosine of the angle between them. It can be calculated using the formula A ⋅ B = |A||B|cosθ, where A and B are the two vectors and θ is the angle between them.

## 5. How can you determine the direction of a vector?

The direction of a vector can be determined by calculating the angle between the vector and a reference axis, typically the positive x-axis. This can be done using trigonometric functions such as sine, cosine, and tangent. Alternatively, the direction can be described using unit vectors, which have a magnitude of 1 and point in the same direction as the original vector.

Replies
5
Views
1K
Replies
19
Views
2K
Replies
3
Views
2K
Replies
18
Views
1K
Replies
4
Views
1K
Replies
4
Views
2K
Replies
7
Views
1K
Replies
21
Views
7K
Replies
56
Views
4K
Replies
11
Views
4K