# Unit Vectors Homework: Vector A-B & Magnitude

• chocolatelover
In summary, the conversation discussed finding the vector A-B and its magnitude, as well as clarifying the difference between magnitude and direction of a vector. The correct solution for A-B is 4i+3j and the magnitude is 5 units. It was also emphasized that magnitude and direction are different characteristics of a vector.
chocolatelover

## Homework Statement

Vector A=3i-1j and B=-i-4j
Find vector A-B and|vector A-B|

## The Attempt at a Solution

Vector A-B=4i-3j

Is the |vector A-B|the magnitude or just the absolute value of the answer?

Thank you very much

|A| is the magnitude of a vector A. To avoid confusion, one can use ||A|| to denote magnitude.

Thank you very much

Is the other part correct? The magnitude is the same thing as the angle of the vector, right? Is there a formula for calculating the magnitude?

Thank you

Last edited:
The magnitude of a vector whose components are <a1, a2> (2 dimensional vector) is:

$$\sqrt{a_1^2 + a_2^2}$$
Please do not confuse magnitude and direction. Although they are both characteristics of a vector, they are different things.

Recheck A-B, the j component has its sign messed up.

Thank you very much

4i+5j does that look correct?

Recheck.
Let A = <a1, a2> and B = <b1, b2>

A-B = <a1-b1, a2-b2>

If vector A=3i-1j
and B=-1i-4j

in order to find A-B, don't you just do 3i--1i=4i and -1i--4j=3j

Wouldn't it be 4i+3j?

and is the magnitude of A-B 6.40?

Thank you

Last edited:
Yup 4i+3j is correct. You made the mistake of writing 4i-3j in your initial post.

Thank you very much

Regards

But your magnitude doesn't look too good. Recheck that.

Thank you

## 1. What is a unit vector?

A unit vector is a vector with a magnitude of 1, which means it has a length of exactly 1 unit. It is used to represent a direction without specifying a specific magnitude or length.

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

The magnitude of a vector can be calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the vector's components. Alternatively, the magnitude can be calculated by taking the absolute value of each component and then using the formula √(x² + y² + z²) for three-dimensional vectors.

## 3. What is the difference between vector A-B and vector B-A?

Vector A-B represents the displacement from point A to point B, while vector B-A represents the displacement from point B to point A. This means that the direction of the vectors will be opposite, but the magnitude will be the same.

## 4. How do you find the unit vector in the same direction as a given vector?

To find the unit vector in the same direction as a given vector, you need to divide the vector by its magnitude. This will result in a vector with a magnitude of 1, pointing in the same direction as the original vector.

## 5. How can unit vectors be used in physics and engineering?

Unit vectors are commonly used in physics and engineering to represent directions and orientations of forces, velocities, and accelerations. They are also used in coordinate systems to define the directions of axes. In addition, unit vectors can be combined with scalar quantities to represent vector quantities, such as displacement, velocity, and acceleration.

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