How to Input a Unit Vector Between X and Y Axes in Mastering Physics

In summary, the conversation discusses the use of unit vectors in Mastering Physics and how to input a unit vector that lies between the X and Y axes. Various methods and calculations are suggested, including using x_unit*y_unit as the unit vector and expressing the vector using its components. After searching online, it is mentioned that i_unit*j_unit = 0, which may affect the previous answer. Eventually, the individual figures out the correct way to write a unit vector that lies 45 degrees from either the x or y axis.
  • #1
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Hi,

I'm wondering if anyone knows how to input a unit vector that lies between X and Y axes, into a Master Physics answering box.

One of the questions I'm working on required a unit vector (to point a direction) to be part of the answer. I know that the direction is between the X and Y axes so I tried using (sqrt0.5,sqrt0.5,0) as my unit vector but that didn't work out. It seems that they want the the unit vector in terms of x_unit, y_unit, z_unit (in mastering physics x_unit = x capped/x with a hat).

Any helps would be greatly appreciated.
 
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  • #2
Should I try using x_unit*y_unit as my unit vector?

I know that x_unit, y_unit, z_unit represent unit vectors in x, y, z directions, respectively. I have only 2 more chances left.

Should I try this -k*(q_0)*(q_3)*y_unit*x_unit/(sqrt((d_2)^2+(d_2)^2))^2

(It's a force in an xy-plane.)
 
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  • #3
gah i hate mastering physics, i had to use it for Mechanics last semester :/

Usually its expressing the vector using it's components such as
w=((x_unit)^2+(y_unit)^2+(z_unit)^2)^1/2
 
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  • #4
After searching on the internet, I found that i_unit*j_unit = 0 so the answer in my previous reply is probably wrong. Anyone?
 
  • #5
QuantumDefect said:
gah i hate mastering physics, i had to use it for Mechanics last semester :/

Usually its expressing the vector using it's components such as
w=((x_unit)^2+(y_unit)^2+(z_unit)^2)^1/2

So would the unit vector in an xy-planet = ((x_unit)^2+(y_unit)^2))^1/2? = (sqrt0.5, sqrt0.5, 0)?

But wouldn't that "w=((x_unit)^2+(y_unit)^2+(z_unit)^2)^1/2" be a scalar quantity? then isn't it no longer a vector and cannot act as a (unit) direction vector?

Thanks in advance
 
  • #6
OK, how about if I ask this. I want to write a unit vector that lies 45 deg. from either x/y axis, interm of unit vectors x_unit and y_unit, is it possible to do that?
 
  • #7
I figured it out, thanks for your help.
 

1. What is a unit vector?

A unit vector is a vector with a magnitude of 1 and is used to represent a direction in space. It is often denoted by a hat symbol (^) on top of the vector's symbol.

2. How do you find the unit vector of a given vector?

To find the unit vector of a given vector, you first need to find the magnitude of the vector. Then, divide each component of the vector by its magnitude. This will give you a vector with the same direction, but a magnitude of 1.

3. What is the importance of unit vectors in mathematics and science?

Unit vectors are important in mathematics and science because they allow us to represent directions and orientations in space. They also make calculations involving vectors and their components easier and more efficient.

4. Can unit vectors be negative?

No, unit vectors cannot be negative. They always have a magnitude of 1 and are only concerned with direction, not magnitude.

5. How are unit vectors used in physics?

In physics, unit vectors are used to represent the direction of forces, velocities, and other physical quantities. They can also be used to break down a vector into its components for easier analysis and calculation.

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