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.mahrap said: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.
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).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.
mahrap said: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.
To clarify what SteamKing wrote, he's talking about vx, vy, and vz, the x-, y-, and z-components of a unit vector v.SteamKing said: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
Vectors are mathematical objects that have both magnitude (size) and direction. They are commonly represented by arrows in diagrams.
Vectors are typically denoted using boldface letters (e.g. a) or by placing an arrow on top of the letter (e.g. a).
In a triangle, the sum of all three sides (represented by vectors a, b, and c) is equal to 0. This is known as the Triangle Law or Parallelogram Law of Vector Addition.
The direction of the third side of a triangle can be determined by using the Triangle Law or Parallelogram Law of Vector Addition. This involves adding the two known sides (vectors a and b) and then finding the negative of that sum (i.e. -a-b). This negative vector represents the opposite direction of the third side (vector c).
Yes, vectors can be used to solve various problems involving triangles such as finding unknown sides or angles, determining the perimeter or area of a triangle, and analyzing the forces acting on an object in a triangular shape. They are a powerful tool in geometry and physics.