Solving Vector Equations w/ A+B+C = 0

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In summary: B| = 11.139i + 19.294jclose, but remember |B|=magnitude=sqrt(a^2+b^2) so you need to find the hypotenuse of the triangle to get |B|, and then use that to find cIn summary, vector A has a magnitude of 11.49 m and points in the negative x direction, while vector B has a magnitude of 19.294 m and points at an angle of 30 degrees above the positive x axis.
  • #1
nokitman
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Homework Statement


Vector A points in the negative x direction. Vector B points at an angle of 30 degrees above the positive x axis. Vector C has a magnitude of 15.0 m and points in a direction 40 degrees below the positive x axis. Given that vectors A + B + C = 0, find the magnitude of vector A and vector B


Homework Equations


Sin = opp/hyp


The Attempt at a Solution


For vector C, I found the x direction to be 11.49 m and the y direction to be -9.64 m.

Other than that I have no idea where to begin.

thanks,
 
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  • #2
nokitman said:

The Attempt at a Solution


For vector C, I found the x direction to be 11.49 m and the y direction to be -9.64 m.

Good. So we know C=11.49i-9.647j

so let's put A=ai+bj. It says A points in the negative x direction, so what should A really be ? (i.e. should the 'a' be +a or -a and what should 'b' equal to?)

So B acts at an angle of 30 degrees to the x-axis. If the magnitude of B is |B| then B=|B|(ci+dj)

so find A+B+C, grouping together the i and j terms.
 
  • #3
like this ?

C = 11.49i - 9.647j
A = ai - bj
B = |B| (ci + dj)
_____________________ +

= (11.49 + a + |B|c)i - (9.647 - b + |C|d)j

Is that right? :confused:
 
  • #4
nokitman said:
like this ?

C = 11.49i - 9.647j
A = ai - bj
B = |B| (ci + dj)
_____________________ +

= (11.49 + a + |B|c)i - (9.647 - b + |C|d)j

Is that right? :confused:

Sorry I made a mistake, let's take out the |B| and just have B=ci+dj

You should get A+B+C = (11.49+a+c)i + (-9.647-b+d)j

once again now, if A=ai+bj is in the negative x direction, what is b equal to? And what sign should the a really have ?
 
  • #5
the "a" should be negative so A=-ai+bj, should the b also be negative?
 
  • #6
nokitman said:
the "a" should be negative so A=-ai+bj, should the b also be negative?

right the 'a' should really be '-a'. So if the j component is the vertical component, and you know A is purely horizontal, what value should 'b' equal to?
 
  • #7
b should be 0 in the A vector

C = 11.49i - 9.647j
A = -ai
B = ci + dj
_________________ +

= (11.49 -a + c)i + (-9.647 + d)j = 0

Is that correct? what's the next step?

Thank you
 
  • #8
nokitman said:
b should be 0 in the A vector

C = 11.49i - 9.647j
A = -ai
B = ci + dj
_________________ +

= (11.49 -a + c)i + (-9.647 + d)j = 0

Is that correct? what's the next step?

Thank you

yes this correct. So if it is equal to zero, that means both the i and j components are zero, so what is d?
 
  • #9
d= oi + oj

how does it get me to find the magnitude of A and B vectors?
 
  • #10
nokitman said:
d= oi + oj

how does it get me to find the magnitude of A and B vectors?

no no

we have A+B+C = = (11.49 -a + c)i + (-9.647 + d)j = 0 =0i+0j.

so when you equate components, what is d equal to?
 
  • #11
d is zero?
 
  • #12
nokitman said:
d is zero?

no if (-9.647 + d) =0 what is d? Do you know why (-9.647 + d) equal 0?
 
  • #13
sorry d is 9.647
 
  • #14
nokitman said:
sorry d is 9.647

ok good. Now we know for a vector say R of magnitude |R|, acting at an angle θ to the x-axis can be represented as R= |R|cosθi+|R|sinθj


Can you now make a similar comparison to the vector B with magnitude |B|? Are you able to see how 'd' relates to |B| at the given angle?
 
  • #15
vector B = |B|cos30i + |B|sin30j ?
is 9.647 the y component of vector B?
 
  • #16
nokitman said:
vector B = |B|cos30i + |B|sin30j ?
is 9.647 the y component of vector B?

yes, so now if d=|B|sin30 -> 9.647=|B|sinn30 what is |B| equal to?

When you get |B|, can you find what 'c' is equal to ?
 
  • #17
|B| = 11.139i + 19.294j?
 

What is a vector equation?

A vector equation is an equation that involves vectors, which are mathematical quantities that have both magnitude and direction.

How do I solve vector equations?

To solve a vector equation, you need to isolate the vector you are looking for on one side of the equation and move all other vectors to the other side. Then, you can use algebraic operations such as addition, subtraction, and multiplication to solve for the unknown vector.

What does A+B+C = 0 mean in a vector equation?

In a vector equation, when A+B+C = 0, it means that the sum of the three vectors A, B, and C is equal to the zero vector, which has no magnitude or direction. This is known as the zero vector property.

Can vector equations be solved using graphing methods?

No, vector equations cannot be solved using graphing methods because vectors are not represented on a traditional x-y coordinate system. Instead, they are represented by directed line segments with a magnitude and direction.

Why are vector equations important in science?

Vector equations are important in science because they allow us to describe and analyze physical quantities, such as velocity and force, that have both magnitude and direction. They are also useful in solving real-world problems involving multiple forces and directions.

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