# Find the angle between this vector and the coordinate axes

Tags:
1. Jun 19, 2017

### donaldparida

1. The problem statement, all variables and given/known data:

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. Relevant 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.

Last edited by a moderator: Jun 19, 2017
2. Jun 19, 2017

### Jamison Lahman

What is the dot product of two vectors in terms of their magnitudes and angle between them? Do you know that formula?

3. Jun 19, 2017

### donaldparida

Yes. Infact i had applied that formula along with this one.

4. Jun 19, 2017

### Jamison Lahman

Posting your work may prove helpful. Have you tried similar methods using cross-products?

5. Jun 19, 2017

### donaldparida

A.B=ABcos(x)
A.B=AxBx+Ay+By
Therefore, ABcos(x)=AxBx+Ay+By
=>cos(x)=(AxBx+Ay+By )/AB

6. Jun 19, 2017

### Jamison Lahman

I agree. There's also the formula,
$$\sin(\theta)=\frac{|\bf{A}\times\bf{B}|}{AB}$$
What about the work using these equations?

7. Jun 19, 2017

### donaldparida

8. Jun 19, 2017

### Jamison Lahman

How about now? My LaTeX is rusty

9. Jun 19, 2017

### donaldparida

Not working. I am getting some weird expression.

10. Jun 19, 2017

### Jamison Lahman

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: Jun 19, 2017
11. Jun 19, 2017

### donaldparida

12. Jun 19, 2017

### Jamison Lahman

Here is a hint: try using r as the hypotenuse of a triangle.

13. Jun 19, 2017

### haruspex

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. Jun 19, 2017

### scottdave

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. Jun 20, 2017

### donaldparida

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. Jun 20, 2017

### Jamison Lahman

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. Jun 20, 2017

### haruspex

Looks right. Much simpler my way though. (Hint: find the tan instead.)