Find the angle between this vector and the coordinate axes

In summary, r vector = 3t i + (4t-5t2)j. Find the angle made by the vector with respect to the x-axis and the y-axis.
  • #1
donaldparida
146
10

Homework Statement

:
[/B]
r vector = 3t i + (4t-5t2)j. Find the angle made by the vector with respect to the x-axis and the y-axis.

2. Homework Equations :

A
.B=AxBx+AyBy

3. The Attempt at a Solution :

I tried to take the dot product of the unit vector along x-axis and r. I did the same for the y-axis but did not get anything useful.
 
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  • #2
donaldparida said:

Homework Statement

: r vector = 3t i + (4t-5t2)j. Find the angle made by the vector with respect to the x-axis and the y-axis.

2. Homework Equations : A.B=AxBx+AyBy
3. The Attempt at a Solution : I tried to take the dot product of the unit vector along x-axis and r. I did the same for the y-axis but did not get anything useful.[/B]
What is the dot product of two vectors in terms of their magnitudes and angle between them? Do you know that formula?
 
  • #3
Yes. In fact i had applied that formula along with this one.
 
  • #4
donaldparida said:
Yes. In fact i had applied that formula along with this one.
Posting your work may prove helpful. Have you tried similar methods using cross-products?
 
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  • #5
A.B=ABcos(x)
A.B=AxBx+Ay+By
Therefore, ABcos(x)=AxBx+Ay+By
=>cos(x)=(AxBx+Ay+By )/AB
 
  • #6
I agree. There's also the formula,
$$\sin(\theta)=\frac{|\bf{A}\times\bf{B}|}{AB}$$
What about the work using these equations?
 
  • #7
I cannot read the equation. Could you please edit it?.
 
  • #8
donaldparida said:
I cannot read the equation. Could you please edit it?.
How about now? My LaTeX is rusty
 
  • #9
Not working. I am getting some weird expression.
 
  • #10
donaldparida said:
Not working. I am getting some weird expression.
I think I have figured it out. Have you tried using trigonometry?

Edit: It should be solvable using strictly trigonometry and also with the vector formulas. Post your work so we can see where you're going wrong.
 
Last edited:
  • #11
I cannot understand how to proceed. Could you please help.
 
  • #12
donaldparida said:
I cannot understand how to proceed. Could you please help.
Here is a hint: try using r as the hypotenuse of a triangle.
 
  • #13
donaldparida said:
A.B=ABcos(x)
A.B=AxBx+Ay+By
Therefore, ABcos(x)=AxBx+Ay+By
=>cos(x)=(AxBx+Ay+By )/AB
Ok, but you have not posted what happened when you applied this to the given vectors. Nobody can tell you where you went wrong, or what to do next, if you do not post your attempt.

Anyway, there is an easier way than using dot or cross products. Just think about the geometry.
 
  • #14
If you had a number for t, (like at t=1 it becomes r = 3i - j ), could you solve that? Write down the steps you would take if it were just a number, then go back and do the same with the expressions. See if that works for you.
 
  • #15
I am getting cos(θ)=3/[sqrt{5(5+5t^2−8t)}]. I am not posting my attempt because it is very lengthy and on top of that i do not know how to type them properly.
 
  • #16
donaldparida said:
I am not posting my attempt because it is very lengthy and on top of that i do not know how to type them properly.
Take a picture of it if you have to. It doesn't seem fair we should do the work and do the work of typing it if you won't put in enough work just to let us help you. It doesn't have to be pretty LaTeX either. As long it is readable in normal text, we can go form there.
 
  • #17
donaldparida said:
I am getting cos(θ)=3/[sqrt{5(5+5t^2−8t)}]. I am not posting my attempt because it is very lengthy and on top of that i do not know how to type them properly.
Looks right. Much simpler my way though. (Hint: find the tan instead.)
 

1. What is the definition of the angle between a vector and the coordinate axes?

The angle between a vector and the coordinate axes is the smallest angle formed between the vector and the positive x-axis or y-axis on a coordinate plane.

2. How do you find the angle between a vector and the x-axis?

To find the angle between a vector and the x-axis, you can use the formula arctan(y/x), where y is the y-component of the vector and x is the x-component of the vector.

3. Can the angle between a vector and the coordinate axes be negative?

No, the angle between a vector and the coordinate axes is always measured as a positive angle. If the vector is in the negative quadrant, the angle can be calculated by subtracting the angle from 360 degrees.

4. How does the direction of a vector affect the angle between the vector and the coordinate axes?

The direction of a vector does not affect the angle between the vector and the coordinate axes. The angle is solely determined by the components of the vector and the axes.

5. Why is the angle between a vector and the coordinate axes important in physics and mathematics?

The angle between a vector and the coordinate axes is important in physics and mathematics because it helps in determining the direction and magnitude of the vector. It also plays a crucial role in solving problems involving vectors and coordinate systems.

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