Perpendicular unit vector

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.
  • #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
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  • #2
well if there is a vector A then vector opposite to A is -A ... changing only x component makes it something different
  • #3
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.

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