# Perpendicular 3Dimensional Vectors

• thursdaytbs
In summary, the conversation discussed different methods for finding a perpendicular vector to two 3-dimensional vectors. The first method mentioned was using the cross product and solving with a determinent. Another method was finding the normal to the plane that contains the two vectors, which was considered the "easy way". The conversation also mentioned a "hard way" of finding a vector with a dot product that vanishes with the first two vectors, which was deemed unnecessary.
thursdaytbs
How would you go about finding a perpendicular vector, to two 3 dimensional vectors? One way, I solved is using the cross product of the two vectors. Splitting the i's j's and k's up and solving using a determinent. But, what's another way to do it?

Find the normal to the plane that contains the two vectors?

whozum said:
Find the normal to the plane that contains the two vectors?

That's the same thing.

thursdaytbs said:
But, what's another way to do it?

You did it "the easy way", which is how I would have done it. "The hard way" would be to find a vector whose dot product with each of the first two vectors vanishes. Pure silliness, that route.

That's the same thing.

Worded differently, might have given him a different idea?

## 1. What are perpendicular 3-dimensional vectors?

Perpendicular 3-dimensional vectors are two vectors in a three-dimensional space that are at a right angle to each other.

## 2. How do you determine if two vectors are perpendicular?

To determine if two vectors are perpendicular, you can use the dot product. If the dot product of two vectors is equal to 0, then the vectors are perpendicular.

## 3. Can two parallel vectors also be perpendicular?

No, two parallel vectors cannot be perpendicular because they lie on the same plane and therefore cannot form a right angle with each other.

## 4. What is the geometric interpretation of perpendicular 3-dimensional vectors?

The geometric interpretation of perpendicular 3-dimensional vectors is that they are orthogonal or perpendicular to each other, and they form the basis for three-dimensional space.

## 5. How are perpendicular 3-dimensional vectors used in real-world applications?

Perpendicular 3-dimensional vectors have various applications in fields such as physics, engineering, and computer graphics. They are used to represent forces, motion, and orientation in three-dimensional space.

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