# Calculating a vector

1. Sep 23, 2015

### astrololo

1. The problem statement, all variables and given/known data
John move 8m 20 degrees north of the west. After, he moves another time 6 m 80 degrees south of the east. Calculate the difference between the two vector of his movement in cartesian form.

2. Relevant equations
Vector =ai +bj

3. The attempt at a solution

By using trigonometry, I found the following triangles : (-7.51, 2.74, 8)
(1.035, -5.91, 6)

So :

D=(1.035i-5.91j)-(-7.51i+2.74j)

D=8.545i-8.65j

I don't know why it isn't workng. I know that my answer isn't good. But I know that my steps are good.

Last edited: Sep 23, 2015
2. Sep 23, 2015

### axmls

What is a degree "north of the south"?

You'll also have to elaborate on the trigonometry you used.

3. Sep 23, 2015

### astrololo

Oh, sorry I meant north of west. Not south. The trigonometry that I used is sin angle =opposite side/ hypoth and cos angle = adjacent side / hypoth to find the composents of my triangle

4. Sep 23, 2015

### HallsofIvy

Staff Emeritus

It's not clear to me what you mean by
What information do those numbers give us about the triangles? Those cannot be lengths of side or angles because they have negative numbers.
You write, as a "relevant equation", "Vector ai+ bj" so I would think that you would be aware that the vector "8m 20 degrees north of the west" gives a= -8 cos(20) and b= 8 sin(20): (-8 cos(20))i+ (8 sin(20))j. Similarly, "6 m 80 degrees south of east" gives 6 cos(80)i- 8 sin(80)j. Add those.

Another way to do this is to draw those two vectors and see that they form two sides of a right triangle of length 6 and 8 with angle between them of 70 degrees.

5. Sep 23, 2015

### astrololo

"What information do those numbers give us about the triangles? Those cannot be lengths of side or angles because they have negative numbers."

Sorry I included the negatives to indicate their direction.

You write, as a "relevant equation", "Vector ai+ bj" so I would think that you would be aware that the vector "8m 20 degrees north of the west" gives a= -8 cos(20) and b= 8 sin(20): (-8 cos(20))i+ (8 sin(20))j. Similarly, "6 m 80 degrees south of east" gives 6 cos(80)i- 8 sin(80)j. Add those.

I think you did an error. It's 6*sin(80) not 8*sin(80). Also, how come that we add them ? I thought that we needed to substract the initial one from the final. I mean, the formula is vector S = vector R - vector R initial (R being the position)

6. Sep 23, 2015

### astrololo

Help please !

7. Sep 23, 2015

### axmls

I'm a little confused by the wording of the question. Typically it would be asking for the vector from the starting point (the origin) to the final position, in which case you would add them. It seems odd to ask for the difference of the two vectors, but if that's the case, I believe your answer is correct.

8. Sep 23, 2015

### astrololo

No, sorry this my error. The question is asking for the final position, not for the difference of final position and initial position. So this is why we're adding the initial position plus the second diplacement of the object.

9. Sep 23, 2015

### axmls

The final position is given by the vector sum of the two vectors you use to get to the final position. That's how we define addition of vectors (just think about how we add two vectors graphically).

10. Sep 23, 2015

### astrololo

Yes, but my mistake was thinking that the question asked for the difference between the final and initial position. (The displacement from initial to final) Now I understand that this wasn't the case.

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