Find the angle between this vector and the coordinate axes

[donaldparida]

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=A_xB_x+A_yB_y

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.

 

[Jamison Lahman]

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=A_xB_x+A_yB_y
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?

 

[donaldparida]

Yes. In fact i had applied that formula along with this one.

 

[Jamison Lahman]

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?

 

[donaldparida]

A.B=ABcos(x)
A.B=A_xB_x+A_y+B_y
Therefore, ABcos(x)=A_xB_x+A_y+B_y
=>cos(x)=(A_xB_x+A_y+B_y )/AB

 

[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?

 

[donaldparida]

I cannot read the equation. Could you please edit it?.

 

[Jamison Lahman]

I cannot read the equation. Could you please edit it?.

How about now? My LaTeX is rusty

 

[donaldparida]

Not working. I am getting some weird expression.

 

[Jamison Lahman]

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.

 

[donaldparida]

I cannot understand how to proceed. Could you please help.

 

[Jamison Lahman]

I cannot understand how to proceed. Could you please help.

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

 

[haruspex]

A.B=ABcos(x)
A.B=A_xB_x+A_y+B_y
Therefore, ABcos(x)=A_xB_x+A_y+B_y
=>cos(x)=(A_xB_x+A_y+B_y )/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.

 

[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.

 

[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.

 

[Jamison Lahman]

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.

 

[haruspex]

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.)