Can you give a more specific question?

In summary, the conversation discusses finding 2 unit vectors, u1 and u2, that lie in the plane x-y+z=0 and are not parallel to each other. The individual has attempted to use the normal vector of the plane, <1,-1,1>, but was told it is not in the plane. They then created a parallel vector but realized the question specifically states they should not be parallel. The expert advises finding values of x, y, and z that satisfy the equation and using them to form unit vectors that are not parallel.
  • #1
kskiraly
5
0

Homework Statement



Find 2 unit vectors u1, u2, lying in the plane, x-y+z=0, which are not parallel to each other.

The Attempt at a Solution



I've tried taking the unit vector of the normal vector <1,-1,1> which is <1/rad(3),-1/rad(3),1/rad(3)>, but my teacher has told me it is not in the plane.

Then for my second vector, I created a parallel vector, but then I reread the question and found out they are not supposed to be parallel.
 
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  • #2
kskiraly said:

Homework Statement



Find 2 unit vectors u1, u2, lying in the plane, x-y+z=0, which are not parallel to each other.

The Attempt at a Solution



I've tried taking the unit vector of the normal vector <1,-1,1> which is <1/rad(3),-1/rad(3),1/rad(3)>, but my teacher has told me it is not in the plane.
Yes, obviously. x- y+ z= (1-(-1)+ 1)/rad(3)= rad(3) not 0! You are aware, I am sure, that the normal vector to a plane is not in the plane! (If you are not, reread the definition of "normal vector".)

Then for my second vector, I created a parallel vector, but then I reread the question and found out they are not supposed to be parallel.
A very good case for always rereading the question (several times)! Yes, it says "not parallel".

To find a vector in the plane x- y+ z= 0, look for values of x, y, z that satisfy that equation. There are, of course, an infinite number of such choices. You can choose any values you like for x and y, for example, and then solve the equation for z. 1 and 0 are good, simple, choices.
If x= 1 and y= 0, then z must satisfy 1- 0+ z= 0.
If x= 0 and y= 1, then z must satisfy 0- 1+ z= 0.

Now form unit vectors from <x, y, z> and show that they are not parallel.
 

1. What is a unit vector?

A unit vector is a vector with a magnitude of 1. It is often used to represent direction and does not change in length when multiplied by a scalar.

2. How are unit vectors represented?

Unit vectors are typically represented using the notation ψ, where the angle symbol represents the vector. They can also be represented using the unit vectors i, j, and k in Cartesian coordinates.

3. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector is a quantity that has both magnitude and direction. Scalars can be added, subtracted, and multiplied, while vectors can also be added and subtracted, but must be multiplied using dot and cross products.

4. How is a plane defined using vectors?

A plane can be defined using two non-parallel vectors that lie in the plane. These vectors can then be used to find the cross product, which represents the normal vector to the plane. The equation of the plane can then be written as Ax + By + Cz = D, where A, B, and C are the components of the normal vector.

5. How are unit vectors used in physics?

In physics, unit vectors are used to represent various physical quantities, such as velocity, acceleration, and force. By using unit vectors, these quantities can be broken down into their respective components and easily manipulated using vector operations.

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