2007-09-25 07:41:24 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Physics
They differ the same way 60 mph differs from 60 mph east. The 60 mph is a scalar, it has no inference or indication of direction. But 60 mph east is a vector because it has both a scalar value, called magnitude, and direction.
Because a vector has direction as well as magnitude (the scalar part), both magnitude and direction have to be accounted for during math operations (e.g., add, subtract, multiply, and divide).
For example, if V = vx + vy = 60 mph east + 60 mph north, what is the magnitude and direction of the resulting velocity V? If you graph these vectors as arrows, we add the two velocities by putting the tail of 60 mph north onto the head of 60 mph east. As a result, V is the hypotenuse of a right triangle formed by the sides of the two added velocities.
Thus, |V|^2 = |vx|^2 + |vy|^2 will get us the magnitude of the sum of vx and vy. |*| means magnitude (the scalar part) of *, whatever * is. Thus |V| = sqrt(2*60^2) = 1.41*60 ~ 84 mph. And the direction of V is simply the angle between V and vx; so that theta = arctan(|vy|/|vx|) = arctan(60/60) = arctan(1) = 45 degrees (or north east). Thus, the sum of the two vector velocities is V = 84 mph at a north-east direction.
Bottom line, vectors have scalar and direction parts; both parts must be taken into consideration when doing math.
2007-09-25 08:18:39 · answer #1 · answered by oldprof 7 · 0⤊ 0⤋
Vectors have a magnitude and direction.
Scalars are just a magnitude
2007-09-25 14:51:29 · answer #2 · answered by ~T 2 · 0⤊ 0⤋
a vector always has 2 components, a magnitude (scalar value) and a direction.
2007-09-25 14:51:50 · answer #3 · answered by Kevin 5 · 0⤊ 0⤋
The same way that going 50 miles an hour north, differs from just going 50 miles an hour.
2007-09-25 14:44:14 · answer #4 · answered by morningfoxnorth 6 · 0⤊ 0⤋
How does positive traction on a 67 Chevy work?...It just does!
2007-09-25 14:50:35 · answer #5 · answered by mnid007 4 · 0⤊ 2⤋