How Do You Calculate Vector Sums and Differences in Physics?

In summary: Also, when subtracting angles, it should be in the form of a - b, not b - a. So it should be 197 - 270 = -73. This mistake led to your incorrect answer for B.In summary, to find the magnitude and angle of a vector, resolve it along the x-axis and y-axis, find the resultant of the x and y components using Pythagoras theorem, and consider the direction of the vector when finding the angle. When subtracting angles, use the form a - b and pay attention to the signs.
  • #1
tjbateh
86
0

Homework Statement



Three vectors a , b , and c each have a magnitude of 42 m and lie in an xy plane. Their directions relative to the positive direction of the x-axis are 29°, 197°, and 314°, respectively. What are (a) the magnitude and (b) the angle of the vector a+ b + c, and (c) the magnitude and (d) the angle of a - b + c? What are (e) the magnitude and (f) the angle of a fourth vector d such that (a + b) - ( c+d ) = 0?

Homework Equations





The Attempt at a Solution



I do not how to approach this problem. Could someone please give me a few steps to try. Would be greatly appreciated!
 
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  • #2
Draw the vectors according their positions. Resolve them along x-axis and y-axis.
Find the resultant of x and y components. And get the final answer using Pythagoras theorem.
Whenever the vector is negatived, reverse the vector and proceed.
 
  • #3
I got A=36.73i + 20.36j
B= -19.07i + (-37.42j)
C= 29.18i + (-32.21j)

a+b+c= 46.84i - 29.27j

It was not correct? Do you see any mistakes?
 
  • #4
tjbateh said:
Do you see any mistakes?
We can't see the mistakes if you don't show your work...
 
  • #5
Ok.

I did 42*cos(29)=36.73
42*sin(29)=20.36

42*cos(63) Got the 63 from 260-197...and that =19.07, which i made negative
42*sin(63)=37.42..also made negative

and..

42*cos(46)..Got the 46 from 360-314...and that = 29.18
42*sin(46)= I just did the calculation, now I'm get 30.21 instead of 32.31...other than that mistake, do you see anything else?
 
  • #6
[42*cos(63) Got the 63 from 260-197...and that =19.07, which i made negative]

This is wrong. It should be 270 - 197
 

Related to How Do You Calculate Vector Sums and Differences in Physics?

1. What are vectors?

Vectors are mathematical quantities that have both magnitude and direction. They are represented by an arrow pointing in the direction of the vector and the length of the arrow represents the magnitude.

2. How are vectors added?

To add vectors, you must first make sure they are in the same dimension. Then, simply add the corresponding components of each vector to get the resulting vector. For example, if vector A is (3, 4) and vector B is (1, 2), then A + B = (3+1, 4+2) = (4, 6).

3. How are vectors subtracted?

Subtracting vectors is similar to adding them. Again, make sure they are in the same dimension and then subtract the corresponding components of the second vector from the first. For example, if vector A is (3, 4) and vector B is (1, 2), then A - B = (3-1, 4-2) = (2, 2).

4. Can vectors be multiplied or divided?

No, vectors cannot be multiplied or divided by each other. However, they can be multiplied or divided by a scalar (a single number). This results in a new vector with the same direction but a different magnitude.

5. How are vectors represented graphically?

Vectors are represented graphically by an arrow pointing in the direction of the vector and the length of the arrow representing the magnitude. They are typically drawn on a coordinate plane with the tail of the arrow at the origin (0, 0).

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