# Parallel Vectors: Solving for a

• MozAngeles
In summary, the problem is to find the value of a that makes the vectors u=<2,4,-5> and v=<-4,-8,a> parallel. Using the equation (uXv)=0, the cross product of the two vectors is 4(a-10)i-2(a-10)j-32k=0. However, the k-hat component is incorrect. An easier method is to solve for u=λv, which should have a single solution for λ and a.
MozAngeles

## Homework Statement

for what value of a will the vectors u=<2,4,-5> and v=<-4,-8,a>

(uXv)=0

## The Attempt at a Solution

i took the cross product and got 4(a-10)i-2(a-10)j-32k=0

i don't know wher eto go from there do i set a-10=0 solve for a so my answer is ten?

You didn't finish writing the problem statement.

Assuming you're trying to find which values of a make the two vectors parralell...

the k-hat component isn't right in what you've posted, and once you get that it's pretty straightforward to find the values of a so that's you get the zero vector as the cross product.

Hi MozAngeles!

There is an easier way to find 2 parallel vectors.
If u and v are parallel, one must be a multiple of the other.

That is, if you try to solve:

u = λv

that should have a single solution for λ and a.

## What are parallel vectors?

Parallel vectors are two or more vectors that have the same direction, but may have different magnitudes or lengths.

## How do you determine if two vectors are parallel?

You can determine if two vectors are parallel by checking if their direction is the same. This can be done by calculating the ratio of the corresponding components of the vectors. If the ratio is the same for all components, then the vectors are parallel.

## How do you solve for the constant "a" in parallel vectors?

To solve for the constant "a" in parallel vectors, you can use the dot product or cross product of the vectors. The dot product of two parallel vectors will be equal to the product of their magnitudes and the cosine of the angle between them. The cross product of two parallel vectors will be equal to zero.

## Can parallel vectors have different magnitudes?

Yes, parallel vectors can have different magnitudes. As long as their direction is the same, they are considered parallel.

## What are some real-life applications of parallel vectors?

Parallel vectors are used in various fields such as physics, engineering, and computer graphics. They are useful for calculating forces, determining the direction of motion, and creating 3D models. They are also used in navigation, such as determining the direction of a plane or ship based on its velocity.

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