2006-08-26 05:22:45 · 9 answers · asked by achal m 1 in Science & Mathematics ➔ Mathematics
Because of the definition of a vector. Where you place the tail of the vector is arbitrary. All that matters is the magnitude and direction of the vector.
This is also a necessary part of vector algebra if vector addition is going to be abelian (order independent). So, for A+B+C to equal A+C+B, it has to work out so that moving the tail of B from the head of A over to the head of A+C doesn't change B.
Finally, the coordinate or decomposition form of a vector always assumes that the tail is at (0,0) and the head is at (x1,y1). So, again, any vectors that would have the same decomposition form have to be equal.
2006-08-26 05:43:58 · answer #1 · answered by tbolling2 4 · 0⤊ 1⤋
I know I am repeating a lot of what others are saying, but I want to add to it:
If two or more vectors are parallel to each other, then they have the same direction. However, they start at different points in space. If they have equal magnitude, then they are equal in distance. If all of these conditions (being parallel to each other, starting a different points, and having equal magnitude) are met, then, by definition, these vectors are equal.
2006-08-26 07:00:47 · answer #2 · answered by dramaman22 3 · 0⤊ 0⤋
a vector is defined by two things:
1- magnitude.
2- direction.
so if two vectors have the same magnitude and direction (parallel) then, they're the same vector actually.
we do not consider where the vector originates from or ends at ( i mean vertexes in space don't count here). it's just a mean to express direction!
2006-08-26 05:36:58 · answer #3 · answered by yoyo 2 · 0⤊ 0⤋
What? You must be kidding but I will humor you.
A vector is defined by its magnitude and direction.
If the vectors are parallel that means they have the same direction.
If the magnitude is the same and their direction is the same then they are equal.
2006-08-26 05:29:45 · answer #4 · answered by Edward 7 · 1⤊ 0⤋
a vector has both magnitude and direction.,
If two vectors are parallel ,then direction for both is same .
For a physical quantity,if there are two vectors having same magnitude as well as same direction ,then both are equal.
2006-08-26 06:26:55 · answer #5 · answered by dilip y 1 · 0⤊ 0⤋
equal vectors are those vectors which has same magnitude and acts in the same direction
2006-08-26 05:30:38 · answer #6 · answered by indian 2 · 0⤊ 0⤋
Yaaaaaaaaaaaaaaaaaaaaaaa
2006-08-26 06:35:47 · answer #7 · answered by avik r 2 · 0⤊ 0⤋
Sometimes they do and sometimes they don't. If you for instance are calculating an equilibrium, it does not matter where the forces act, only in what direction.
2006-08-26 05:36:01 · answer #8 · answered by Anonymous · 0⤊ 0⤋
Why wouldn't they be?
2006-08-26 06:14:13 · answer #9 · answered by Krzysztof_98 2 · 0⤊ 0⤋