# Perpendicular unit vector

• TW Cantor
In summary, to find the unit vector perpendicular to the plane containing vectors a and b, we can use the formula (a*b)/(|a*b|). After plugging in the values for a and b, the resulting unit vector is (-0.6438i + 0.008j - 0.7651k). To ensure a positive x component, we can take the opposite of this vector, resulting in a final answer of (0.644i + 0.008j - 0.765k). This can be verified by checking if the magnitude of this vector is approximately 1.

## Homework Statement

Given that a = (-1,16,-1) and b = (-18,-15,-15),

find the unit vector which is perpendicular to the plane containing a and b.

There are two possible answers. Choose the answer with a positive x component.

## Homework Equations

(a*b) = (a2*b3-a3*b2)i - (a1*b3-a3*b1)j - (a1*b2-a2*b1)k

(a*b)/(|a*b|) = unit vector

## The Attempt at a Solution

using the above formula i worked out (a*b)= -255i + 3j - 303K

the modulus of a*b is therefore: sqrt(2552 + 32 + 3032)

i then put these values into the equation and i get:

-0.6438i + 0.008j - 0.7651k

since i need to make it positive in the x component my final answer is:

0.644i + 0.008 - 0.765k

am i doing this correctly? it just seems like a very unusual numbers

well if there is a vector A then vector opposite to A is -A ... changing only x component makes it something different

you can always check if its a unit vector or not,its magnitude should be 1

as this one's mag in approx 1.01 .. i guess your answer is correct

## What is a perpendicular unit vector?

A perpendicular unit vector is a vector that is perpendicular (or at a 90 degree angle) to another vector and has a magnitude of 1. It is often used in mathematics and physics to represent direction and is an important concept in vector calculus.

## How do you find the perpendicular unit vector of a given vector?

To find the perpendicular unit vector of a given vector, you can use the cross product or dot product of the vector. The cross product will give you a vector that is perpendicular to both the given vector and another vector, while the dot product will give you a vector that is perpendicular to only the given vector.

## What is the importance of perpendicular unit vectors in physics?

Perpendicular unit vectors are important in physics because they represent direction in three-dimensional space. They are used in various physical equations, such as calculating torque, angular momentum, and electromagnetic fields.

## Can a vector have more than one perpendicular unit vector?

No, a vector can only have one perpendicular unit vector. This is because a perpendicular unit vector is unique and is determined by the direction of the given vector.

## How are perpendicular unit vectors used in computer graphics?

In computer graphics, perpendicular unit vectors are used to represent the orientation of objects in three-dimensional space. They are also used in lighting calculations to determine the direction and intensity of light on a surface.