Calculate absolute value of A+B

[tnhoots]

Homework Statement

Consider two vectors by A=5i-3j and B=-i - 2j
Calculate A+B
Calculate A-B
Calculate absolute value of A+B
Calculate absolute value of A-B

Homework Equations

R= (Ax + Bx)i + (Ay + By)j
R= (Ax + Bx)i - (Ay + By)j

The Attempt at a Solution

I'm not sure where to start with this problem. I know the equations to use. But its figuring out what value goes where that is hindering me

 

[Kurdt]

For the first two you have written the equations you need almost (The subtraction equation needs modifying). What is stopping you plugging in A_x and B_x etc. For parts 3 and 4 do you know how to calculate the absolute value of a vector?

 

[tnhoots]

still working

I found the solution to part A. For part B I am putting the numbers into the equation B+(-A). It looks like this (-1-5)+(-2+3) and I get -6i+1j. However, that appears to be wrong. I don't know how to do the absolute value of a vector. And I also don't know how to find the direction of A+B and A-B.

 

[Kurdt]

When adding vectors we have as you have above:

\mathbf{C}=(A_x +B_x) \mathbf{\hat{i}} + (A_y +B_y)\mathbf{\hat{j}}

For vector subtraction or vector difference we have:

\mathbf{C}=(A_x -B_x) \mathbf{\hat{i}} + (A_y -B_y)\mathbf{\hat{j}}

The absolute value is given by pythagorean theorem.

|\mathbf{A}| = \sqrt{A_x^2+A_y^2}

 

[tnhoots]

Ok...still a little confused on the absolute value thing.
For the absolute value of A+B I found the absolute value of A which is square root of 34=5.83. Then found the absolute value of B which is square root of 5=2.236. Then I added those together. I did the same for the absolute value of A-B except i subtracted them instead of adding them. However, this isn't right. Where am I going wrong?

I am also confused on how to find the direction of A+B and A-B. I thought that you found the direction of something by taking the tangent(-1) of y/x. However, I did that on a problem where y=35.0 and x=-22.5 and got the answer to be -57.3 and this was wrong...Isn't that the correct way though?

 

[Kurdt]

With regards to the absolute value, you have done it wrong. What you need to do is take the absolute value of the new vector which is A+B or A-B.

I'm not sure about your second question because A+B and A-B are vectors they already have direction. Are you talking about finding a specific angle relative to one of the axes?

 

[tnhoots]

So I would take the absolute value of A+B which was 4i+-5j? I would do that by taking the square root of (4squared + -5squared)? And do the same for the absolute value of A-B which was 6i + -1j? Would I subtract those square roots? And the question about their direction wanted to know what there direction would be in degrees from the positive x axis.

 

[Kurdt]

That is correct except you would not subtract the square roots for the A-B vector you would add them as normal.

If you want the angle from the positive x-axis, then taking the inverse tangent of y/x is a method to follow but you have to be careful because you have to add some degrees on depending which quadrant the point is in.

 

[tnhoots]

could you elaborate on finding the degrees from the positive x axis. I am not told what quadrant anything is in...

 

[tnhoots]

I have a similar problem about finding the position from the x-axis. In this problem y is 35.0 and x is -22.5. So wouldn't I take the inverse tangent of 35.0/-22.5? This is my thinking but my answer of -57.3 is incorrect.

 

[tnhoots]

Alright, so I figured out the direction of the A+B and A-B. However, when i do the exact same thing for the second problem where x=-22.5 and y=35.0 it is wrong. Would i not take the inverse tangent of 35.0/-22.5. I find this to be
-57.26 degrees from the positive x-axis. Why isn't that correct?

 

[HallsofIvy]

could you elaborate on finding the degrees from the positive x axis. I am not told what quadrant anything is in...

I have a similar problem about finding the position from the x-axis. In this problem y is 35.0 and x is -22.5. So wouldn't I take the inverse tangent of 35.0/-22.5? This is my thinking but my answer of -57.3 is incorrect.

Are you required to do that? You stated the problem as
"Consider two vectors by A=5i-3j and B=-i - 2j
Calculate A+B
Calculate A-B
Calculate absolute value of A+B
Calculate absolute value of A-B"

None of those require finding a direction.

However, to answer your question, look at the specific x and y values. x= -22.5 and y= 35.0 so you are in the second quadrant. You -57.3 degrees is from the negative x-axis. The angle from the positive x-axis is 180- 57.3= 122.7 degrees.

 

[tnhoots]

Yes, I was. However I found the correct solution to that one. However, I have a similar problem that wants to know the degrees from the positive x-axis of a vector with components x=-22.5 and y=35.0. I did the inverse tangent of 35.0/-22.5 and find it to be -57.26 degrees from the positive x-axis. Why isn't that correct?

 

[Kurdt]

Yes, I was. However I found the correct solution to that one. However, I have a similar problem that wants to know the degrees from the positive x-axis of a vector with components x=-22.5 and y=35.0. I did the inverse tangent of 35.0/-22.5 and find it to be -57.26 degrees from the positive x-axis. Why isn't that correct?

Thats explained by HallsofIvy above. The angle you calculated was from the negative x-axis not the positive so you need to correct it.

 

[tnhoots]

THANKS! I think I may finally be getting the hang of this!