Draw the vectors head to tail so they make a triangle

In summary, the conversation is about drawing vectors head to tail to create a triangle and using trigonometry to find the sides and angles of the triangle. The person is not sure how to draw the vectors and is used to using vector addition but is now considering using the laws of sine and cosine. The expert suggests looking at the problem as a triangle and using the given information to find the missing angles and sides. The person also asks about how to determine the direction of the triangle, to which the expert explains that there is not enough information to determine that. The expert also confirms that the same method can be used for other similar problems.
  • #1
Maximillien
8
0
Draw the vectors head to tail so they make a triangle
 
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  • #2
Start with the first one. Draw the vectors head to tail so they make a triangle. The information they are giving you tells you some sides and angles in the triangle. Use trig.
 
  • #3
Ya that's the part I don't know how to do

Because it # 11 it gives you Vector a = 5 cm long (the magnitude I believe) then it says C or the Resultant is also 5.0 cm long and the angle between A and C is 70 degrees I have no idea how to draw that. I'm used to going in the fashion of Vector A (polar or rectangular) + Vector B (polar or rectangular) + C (polar or rectangular) .. = Resultant

or using the unit vector notation... And for these problems would I have to use the laws of sine and cosine or could I just do it with a vector additon method.
 
  • #4
Look at the second picture here. http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html. Relabel R to C. That's the picture you should have. It's a triangle. Now fix the lengths and angles you match what you have. Looks to me like an isosceles triangle with side A=side C and an angle of 70 degrees between then. I would find the other angles just using that the sum of all of angle of a triangle is 180. Etc. Sure use things like the law of sines and law of cosines. You can't just directly use a vector addition method because you aren't given any components to add.
 
  • #5
Ya I always draw triangles just like that

my problem is they only give the magnitude i believe for A and the magnitude for the resultant so how can I know in what direction the triangles should go ?
 
  • #6
Maximillien said:
my problem is they only give the magnitude i believe for A and the magnitude for the resultant so how can I know in what direction the triangles should go ?

You don't have to know that. They are only asking you for the magnitude of B and it's relative angles with the other vectors. You can't know anything about say, the orientation of the triangle. They don't give you enough information to determine that.
 
  • #7
So would I use the same method to solve the other #'s ? Thanks a million Dick.
 
  • #8
Where did the first post go? It just shows dots now... :confused:
 

1. What is the purpose of drawing vectors head to tail to make a triangle?

The purpose of drawing vectors head to tail to make a triangle is to visually represent the vector addition process. This method allows us to see the resultant vector, which is the sum of the individual vectors, and its direction and magnitude.

2. How do I draw vectors head to tail to make a triangle?

To draw vectors head to tail to make a triangle, start by drawing the first vector as an arrow pointing in a specific direction. Then, draw the second vector starting from the tip of the first vector and pointing in its own direction. Finally, draw the third vector starting from the tip of the second vector and pointing back to the starting point of the first vector. The triangle formed by the three vectors represents the resultant vector.

3. Can I draw more than three vectors to make a triangle?

Yes, you can draw any number of vectors to make a triangle. The process remains the same - start from the tip of the previous vector and point in the direction of the next vector. The triangle formed by the last vector will represent the resultant vector.

4. How do I calculate the magnitude and direction of the resultant vector using this method?

To calculate the magnitude and direction of the resultant vector, we can use the Pythagorean theorem and trigonometric functions. The length of the resultant vector is equal to the square root of the sum of the squares of the individual vectors' lengths. The direction can be found using the inverse tangent function, where the opposite side is the y-component of the resultant vector and the adjacent side is the x-component of the resultant vector.

5. What are some real-life applications of drawing vectors head to tail to make a triangle?

One real-life application of this method is in navigation, where multiple forces or velocities are acting on a moving object. By visually representing these vectors as a triangle, we can determine the resultant direction and speed of the object. This method is also useful in physics and engineering to calculate the net force or displacement of an object under multiple influences.

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