# Find a vector in the opposite direction with double the length?

• dylanhouse
In summary, to find a vector in the opposite direction of PQ that has twice the length of PQ, you simply multiply the vector PQ by -2. Finding the length of PQ is not necessary for this solution.
dylanhouse

## Homework Statement

Find a vector in the opposite direction of PQ that has twice the length of PQ.

PQ= [-9]
| 6|
| 0|
[ 2]

## The Attempt at a Solution

I found the length of PQ to be 11. To answer the question, do I just multiply the vector PQ by -2?

hi dylanhouse!
dylanhouse said:
I found the length of PQ to be 11. To answer the question, do I just multiply the vector PQ by -2?

yup!

it's that simple!

(oh, and you didn't need to find the length at all … but i expect you spotted that)

Thanks so much! I had first used a unit vector but that didn't work out!

## 1. What is a vector?

A vector is a mathematical object that represents both magnitude and direction. It is often used in physics and engineering to describe the movement or force acting on an object.

## 2. How do you find a vector in the opposite direction?

To find a vector in the opposite direction, you can simply multiply all of its components by -1. This will reverse the direction of the vector without changing its magnitude.

## 3. What does it mean to have a vector with double the length?

A vector with double the length means that the magnitude of the vector has been multiplied by 2. This will result in a longer vector with the same direction as the original vector.

## 4. Can you give an example of finding a vector in the opposite direction with double the length?

Yes, for example, if we have a vector with components (3,4), its opposite direction would be (-3,-4). To find a vector with double the length, we would multiply the components by 2, resulting in (6,8).

## 5. Why would someone need to find a vector in the opposite direction with double the length?

This could be useful in various situations, such as finding the displacement of an object that has changed direction or calculating the force needed to move an object in the opposite direction with double the speed. It is also a common practice in vector addition and subtraction.

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