Describing the Vector <t,t> for All Real Numbers: Homework Help

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In summary, the vector t<1,1> where t is all real numbers produces a line with a slope of 1 on the xy plane. The vector has a magnitude and direction determined by the value of t.
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RJLiberator

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Homework Statement


Describe...
t<1,1> where t is all real numbers.

Homework Equations

The Attempt at a Solution



I start by multiplying t to each x and y component.
The resulting vector (field??) is <t,t> where t is all real numbers.

Does this mean that the 'image' is the entire xy plane of all real numbers?
 
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  • #2
Try plotting a few points for various ##t##.
 
  • #3
Oh... brain cramp.
t can be any real number, but it must be only one real number.
So you get a slice through the xy plane.

(1,1)
(2,2)
This is y=x which has a slope of 1.
Correct?
 
  • #4
You could call t a "scalar" meaning it only affects the magnitude of the vector, not it's direction. So what direction is your vector pointing? What's the magnitude?
 
  • #5
RJLiberator said:
This is y=x which has a slope of 1.
Correct?

Yep. All vectors t<1,1> lie on the line y=x
 
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1. What is a vector?

A vector is a mathematical object that represents both magnitude (size) and direction. It is commonly used in physics and engineering to describe quantities such as displacement, velocity, and force.

2. How do you describe a vector?

A vector is typically described using its magnitude and direction. For example, a vector with a magnitude of 5 units and a direction of 30 degrees above the horizontal would be written as 5 units at 30 degrees.

3. What are the components of a vector?

A vector has two components: magnitude and direction. The magnitude is a numerical value that represents the size or length of the vector, and the direction is the angle at which the vector is pointing.

4. Can a vector have a negative magnitude?

Yes, a vector can have a negative magnitude. This indicates that the vector is pointing in the opposite direction of its positive magnitude counterpart. For example, a vector with a magnitude of -5 units and a direction of 45 degrees would be pointing in the opposite direction of a vector with a magnitude of 5 units and a direction of 45 degrees.

5. How is a vector represented?

A vector is typically represented graphically using an arrow, with its tail starting at the origin and its head pointing in the direction of the vector. The length of the arrow represents the magnitude of the vector, and the angle of the arrow represents the direction.

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