Question

Two vectors are equal if and only if they have the same magnitude and __________

Answer 1

What is the difference from a vector and an arbitrary line segment?

Answer 2

A vector denotes a magnitude and direction. Arbitrary line segment does not form a ray, which a vector will always point in a direction where the length of the line can stand for the magnitude of the force being conveyed.

Answer 3

Two vectors are the same when thier magnitude (absolute value) are equal, and the direction are equal. The direction is often portrayed in it's coordinate form in 2D by x and y, and 3D by x, y and z. The length, at least in physics, is usually portraying the velocity of the vector. When you have velocity (magnitude-scalar) and direction (scalar) combined, you have a vector.

Answer 4

Hope this helps bud.

Answer 5

A magnitude is always positive definite, isn't it? That is, <x,x> >= 0 with equality if and only if x is the zero vector.