# Find the angle between 2 vectors w=i+3j, vector v=<5, 2>

• MHB
• Elissa89
In summary, a vector is a mathematical object with both magnitude and direction, represented by an arrow. The angle between two vectors is the measure of rotation needed to align them, and can be found using the dot product formula. It is also possible to find the angle between two vectors if only their components are known, by first finding their magnitudes. The dot product is equal to the product of the magnitudes and the cosine of the angle, making it useful for finding the angle between vectors.
Elissa89
I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta).

vector w=i+3j

vector v=<5, 2>

Elissa89 said:
I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta).

vector w=i+3j

vector v=<5, 2>

find the cosine, then use a form of the Pythagorean identity ...

$\sin{t} = \sqrt{1-\cos^2{t}}$

## What is the definition of vector?

A vector is a mathematical object that has both magnitude and direction. It is represented by an arrow pointing in a specific direction and its length represents the magnitude.

## What is the angle between two vectors?

The angle between two vectors is the measure of the rotation that is needed to align one vector with the other. It is usually measured in degrees or radians.

## How do you find the angle between two vectors?

To find the angle between two vectors, you can use the dot product formula: cosθ = (a∙b) / (|a|∙|b|), where a and b are the two vectors and θ is the angle between them.

## Can you find the angle between two vectors if you only know their components?

Yes, you can find the angle between two vectors if you only know their components. You can use the same dot product formula, but first you need to find the magnitudes of the vectors using the Pythagorean theorem.

## What is the relationship between the dot product and the angle between two vectors?

The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them. This means that the dot product can help us find the angle between two vectors.

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