Vectors! how are a,b,c in a+b+c=0 a triangle

1. Dec 11, 2012

mahrap

a, b, and c are unit vectors and a+b+c=0. This is the first part of a question and the solution involves the fact that a, b, and c form a triangle. I am having a really hard time how these vectors form a triangle. Can you pleases be as thorough as possible in your answer. Thank you so much for all the help.

2. Dec 11, 2012

mahrap

a, b, and c are unit vectors and a+b+c=0. This is the first part of a question and the solution involves the fact that a, b, and c form a triangle. I am having a really hard time how these vectors form a triangle. Can you pleases be as thorough as possible in your answer.

Are they unit vectors such as a = <1,0,0> b=<0,1,0> and c=<0,0,1>. But how would that =0?

Thank you so much for all the help.

3. Dec 11, 2012

SteamKing

Staff Emeritus
Unit vectors can be other ones than the a, b, and c in your original post.

If a vector has components vx, vy, and vz, a unit vector is one in which
vx^2+vy^2+vz^2 = 1

4. Dec 11, 2012

lewando

Try adding these vectors graphically, using the head-to-tail method, such that the resultant is a vector with zero magnitude.

5. Dec 11, 2012

HallsofIvy

Staff Emeritus
What do you think "a+ b+ c" means for vectors? Draw a vector and call it "a". Draw another vector and call it "b". "a+ b" means the tail of vector b is attached to the tip of vector b. "a+ b" is the vector whose tail is at the tail of "a" and whose tip is at the tip of "b". And, the, of course, "a+ b+ c" means we have another vector, "c", whose tail is attached to the vector "b". That sum. "a The "0" vector has no length its "tail" is the same as its "tip". Saying that "a+ b+ c= 0" means that the tail of vector "a" (which is the tail of "a+ b+ c" and the tip of "c" (which is the tip of "a+ b+ c") are the same point. That means that the three vectors form a triangle.

No, precisely because they do not add to 0, they add to <1, 1, 1>. But, for example, a= <1/2, 1, 0>, <1/2, -1, 0>, <-1, 0, 0> add to 0 and, geometrically, they form the triangle with vertices at (0, 0, 0), (1/2, 1, 0), and (1, 0, 0).

(Yes, I did that in two dimensions just because it is easier- and a triangle is, after all, a two dimensional figure.)

6. Dec 11, 2012

Staff: Mentor

To clarify what SteamKing wrote, he's talking about vx, vy, and vz, the x-, y-, and z-components of a unit vector v.

Regarding the triangle, if the vectors can be arranged, head-to-tail, so that they start and end at the same point, the sum of the vectors is zero.